Strong interactions in many-body quantum systems complicate the interpretation of charge transport in such materials. To shed light on this problem, we study transport in a clean quantum system: ultracold 6Li in a two-dimensional (2D) optical lattice, a testing ground for strong interaction physics in the Fermi-Hubbard model. We determine the diffusion constant by measuring the relaxation of an imposed density modulation and modeling its decay hydrodynamically. The diffusion constant is converted to a resistivity using the Nernst-Einstein relation. That resistivity exhibits a linear temperature dependence and shows no evidence of saturation, two characteristic signatures of a bad metal. The techniques we develop here may be applied to measurements of other transport quantities, including the optical conductivity and thermopower.

%B Science %G eng %U http://science.sciencemag.org/content/early/2018/12/06/science.aat4134 %R 10.1126/science.aat4134 %0 Journal Article %J Phys. Rev. B %D 2018 %T Electronic and magnetic properties of the candidate magnetocaloric-material double perovskites $\mathrmLa}_2\mathrmMnCoO}_6$, $\mathrmLa}_2\mathrmMnNiO}_6$, and $\mathrmLa}_2\mathrmMnFeO}_6$ %A Gauvin-Ndiaye, C. %A Baker, T. E. %A Karan, P. %A Massé, É. %A Balli, M. %A Brahiti, N. %A Eskandari, M. A. %A P. Fournier %A A.-M. S. Tremblay %A Nourafkan, R. %B Phys. Rev. B %V 98 %P 125132 %8 Sep %G eng %U https://link.aps.org/doi/10.1103/PhysRevB.98.125132 %R 10.1103/PhysRevB.98.125132 %0 Journal Article %J Phys. Rev. B %D 2018 %T Hall and Faraday effects in interacting multiband systems with arbitrary band topology and spin-orbit coupling %A Nourafkan, R. %A A.-M. S. Tremblay %B Phys. Rev. B %V 98 %P 165130 %8 Oct %G eng %U https://link.aps.org/doi/10.1103/PhysRevB.98.165130 %R 10.1103/PhysRevB.98.165130 %0 Journal Article %J Phys. Rev. B %D 2017 %T Effect of nonsymmorphic space groups on correlation functions in iron-based superconductors %A Nourafkan, R. %A A.-M. S. Tremblay %B Phys. Rev. B %V 96 %P 125140 %8 Sep %G eng %U https://link.aps.org/doi/10.1103/PhysRevB.96.125140 %R 10.1103/PhysRevB.96.125140 %0 Journal Article %J Phys. Rev. B %D 2017 %T Effects of interaction strength, doping, and frustration on the antiferromagnetic phase of the two-dimensional Hubbard model %A Fratino, L. %A Charlebois, M. %A Sémon, P. %A Sordi, G. %A A.-M. S. Tremblay %B Phys. Rev. B %V 96 %P 241109(R) %8 Dec %G eng %U https://link.aps.org/doi/10.1103/PhysRevB.96.241109 %R 10.1103/PhysRevB.96.241109 %0 Journal Article %J Phys. Rev. B %D 2017 %T Hall effect in cuprates with an incommensurate collinear spin-density wave %A Charlebois, M. %A Verret, S. %A Foley, A. %A Simard, O. %A D. Sénéchal %A A.-M. S. Tremblay %B Phys. Rev. B %V 96 %P 205132 %8 Nov %G eng %U https://link.aps.org/doi/10.1103/PhysRevB.96.205132 %R 10.1103/PhysRevB.96.205132 %0 Journal Article %J Phys. Rev. B %D 2017 %T Maximum entropy analytic continuation for frequency-dependent transport coefficients with nonpositive spectral weight %A Reymbaut, A. %A Gagnon, A.-M. %A Bergeron, D. %A A.-M. S. Tremblay %B Phys. Rev. B %V 95 %P 121104 %8 Mar %G eng %U http://link.aps.org/doi/10.1103/PhysRevB.95.121104 %R 10.1103/PhysRevB.95.121104 %0 Journal Article %J Phys. Rev. B %D 2017 %T Orbital effect of the magnetic field in dynamical mean-field theory %A Acheche, S. %A Arsenault, L.-F. %A A.-M. S. Tremblay %B Phys. Rev. B %V 96 %P 235135 %8 Dec %G eng %U https://link.aps.org/doi/10.1103/PhysRevB.96.235135 %R 10.1103/PhysRevB.96.235135 %0 Journal Article %J Phys. Rev. B %D 2017 %T Phenomenological theories of the low-temperature pseudogap: Hall number, specific heat, and Seebeck coefficient %A Verret, S. %A Simard, O. %A Charlebois, M. %A D. Sénéchal %A A.-M. S. Tremblay %B Phys. Rev. B %V 96 %P 125139 Editor's choice %8 Sep %G eng %U https://link.aps.org/doi/10.1103/PhysRevB.96.125139 %R 10.1103/PhysRevB.96.125139 %0 Journal Article %J Phys. Rev. B %D 2017 %T Signatures of the Mott transition in the antiferromagnetic state of the two-dimensional Hubbard model %A Fratino, L. %A Sémon, P. %A Charlebois, M. %A Sordi, G. %A A.-M. S. Tremblay %B Phys. Rev. B %V 95 %P 235109 %8 Jun %G eng %U https://link.aps.org/doi/10.1103/PhysRevB.95.235109 %R 10.1103/PhysRevB.95.235109 %0 Journal Article %J Phys. Rev. B %D 2017 %T Subgap structures and pseudogap in cuprate superconductors: Role of density waves %A Verret, S %A Charlebois, M %A D. Sénéchal %A A.-M. S. Tremblay %XIn scanning tunneling microscopy conductance curves, the superconducting gap of cuprates is sometimes accompanied by small subgap structures at very low energy. This was documented early on near vortex cores and later at zero magnetic field. Using mean-field toy models of coexisting d-wave superconductivity, d-form-factor density wave, and extended s-wave pair density wave (s PDW), we find agreement with this phenomenon, with s PDW playing a critical role. We explore the high variability of the gap structure with changes in band structure and density wave (DW) wave vector, thus explaining why subgap structures may not be a universal feature in cuprates. In the absence of nesting, nonsuperconducting results never show signs of pseudogap, even for large density wave magnitudes, therefore reinforcing the idea of a distinct origin for the pseudogap, beyond mean-field theory. Therefore, we also briefly consider the effect of DWs on a preexisting pseudogap.

%B Phys. Rev. B %V 95 %P 054518 %G eng %R 10.1103/PhysRevB.95.054518 %0 Magazine Article %D 2017 %T Taming High-temperature superconductivity %A A.-M. S. Tremblay %A A. Chubukov %K Cuprates %K High-temperature superconductivity %K review %K theory %B CERN Courier %V 57 %P 43 %8 09/2017 %G eng %U http://cerncourier.com/cws/download/Sep17 %N 7 %9 Magazine Article %0 Journal Article %J Phys. Rev. E %D 2016 %T Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation %A Bergeron, Dominic %A A.-M. S. Tremblay %B Phys. Rev. E %V 94 %P 023303 %8 Aug %G eng %U http://link.aps.org/doi/10.1103/PhysRevE.94.023303 %R 10.1103/PhysRevE.94.023303 %0 Journal Article %J Phys. Rev. B %D 2016 %T Antagonistic effects of nearest-neighbor repulsion on the superconducting pairing dynamics in the doped Mott insulator regime %A Reymbaut, A. %A Charlebois, M. %A Asiani, M. Fellous %A Fratino, L. %A Sémon, P. %A Sordi, G. %A A.-M. S. Tremblay %B Phys. Rev. B %V 94 %P 155146 %8 Oct %G eng %U http://link.aps.org/doi/10.1103/PhysRevB.94.155146 %R 10.1103/PhysRevB.94.155146 %0 Journal Article %J Phys. Rev. Lett. %D 2016 %T Correlation-Enhanced Odd-Parity Interorbital Singlet Pairing in the Iron-Pnictide Superconductor LiFeAs %A Nourafkan, R. %A Kotliar, G. %A A.-M. S. Tremblay %B Phys. Rev. Lett. %V 117 %P 137001 %8 Sep %G eng %U http://link.aps.org/doi/10.1103/PhysRevLett.117.137001 %R 10.1103/PhysRevLett.117.137001 %0 Journal Article %J Phys. Rev. B %D 2016 %T Mott transition and magnetism on the anisotropic triangular lattice %A Acheche, S. %A Reymbaut, A. %A Charlebois, M. %A D. Sénéchal %A A.-M. S. Tremblay %B Phys. Rev. B %V 94 %P 245133 %8 Dec %G eng %U http://link.aps.org/doi/10.1103/PhysRevB.94.245133 %R 10.1103/PhysRevB.94.245133 %0 Journal Article %J Scientific reports %D 2016 %T An organizing principle for two-dimensional strongly correlated superconductivity. %A Fratino, L %A Sémon, P %A Sordi, G %A A.-M. S. Tremblay %XSuperconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature , the maximum of the condensation energy as a function of doping, the correlation between maximum and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state.

%B Scientific reports %V 6 %P 22715 %G eng %U http://www.ncbi.nlm.nih.gov/pubmed/26964524 http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=PMC4786811 %R 10.1038/srep22715 %0 Journal Article %J Phys. Rev. B %D 2016 %T Pseudogap and superconductivity in two-dimensional doped charge-transfer insulators %A Fratino, L. %A Sémon, P. %A Sordi, G. %A A.-M. S. Tremblay %B Phys. Rev. B %V 93 %P 245147 %8 06/2016 %G eng %U http://link.aps.org/doi/10.1103/PhysRevB.93.245147 %R 10.1103/PhysRevB.93.245147 %0 Journal Article %J Phys. Rev. B %D 2015 %T Antiferromagnetism in the Hubbard model on the honeycomb lattice: A two-particle self-consistent study %A Arya, S. %A Sriluckshmy, P. V. %A Hassan, S. R. %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 92 %P 045111 %8 Jul %U http://link.aps.org/doi/10.1103/PhysRevB.92.045111 %R 10.1103/PhysRevB.92.045111 %0 Journal Article %J Phys. Rev. X %D 2015 %T d-wave superconductivity in the frustrated two-dimensional periodic Anderson model %A Wu, Wei %A A.-M. S. Tremblay %B Phys. Rev. X %I American Physical Society %V 5 %P 011019 %8 Feb %U http://link.aps.org/doi/10.1103/PhysRevX.5.011019 %R 10.1103/PhysRevX.5.011019 %0 Journal Article %J Phys. Rev. B %D 2015 %T Impurity-induced magnetic moments on the graphene-lattice Hubbard model: An inhomogeneous cluster dynamical mean-field theory study %A Charlebois, M. %A D. Sénéchal %A Gagnon, A.-M. %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 91 %P 035132 %8 Jan %U http://link.aps.org/doi/10.1103/PhysRevB.91.035132 %R 10.1103/PhysRevB.91.035132 %0 Journal Article %J Phys. Rev. B %D 2015 %T Maximum entropy analytic continuation for spectral functions with nonpositive spectral weight %A Reymbaut, A. %A Bergeron, D. %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 92 %P 060509 %8 Aug %U http://link.aps.org/doi/10.1103/PhysRevB.92.060509 %R 10.1103/PhysRevB.92.060509 %0 Journal Article %J Phys. Rev. B %D 2015 %T Superconducting dome in doped quasi-two-dimensional organic Mott insulators: A paradigm for strongly correlated superconductivity %A Hébert, Charles-David %A Sémon, Patrick %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 92 %P 195112 %8 Nov %U http://link.aps.org/doi/10.1103/PhysRevB.92.195112 %R 10.1103/PhysRevB.92.195112 %0 Journal Article %J Phys. Rev. B %D 2014 %T Electric polarization of S$_0.5$Ba$_0.5$MnO$_3$: A multiferroic Mott insulator %A Nourafkan, R. %A Kotliar, G. %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 90 %P 220405 %8 Dec %U http://link.aps.org/doi/10.1103/PhysRevB.90.220405 %R 10.1103/PhysRevB.90.220405 %0 Journal Article %J Phys. Rev. B %D 2014 %T Ergodicity of the hybridization-expansion Monte Carlo algorithm for broken-symmetry states %A Sémon, P. %A Sordi, G. %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 89 %P 165113 %8 Apr %U http://link.aps.org/doi/10.1103/PhysRevB.89.165113 %R 10.1103/PhysRevB.89.165113 %0 Journal Article %J Phys. Rev. B %D 2014 %T Lazy skip-lists: An algorithm for fast hybridization-expansion quantum Monte Carlo %A Sémon, P. %A Yee, Chuck-Hou %A Haule, Kristjan %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 90 %P 075149 %8 Aug %U http://link.aps.org/doi/10.1103/PhysRevB.90.075149 %R 10.1103/PhysRevB.90.075149 %0 Journal Article %J Phys. Rev. B %D 2014 %T Orbital magnetization of correlated electrons with arbitrary band topology %A Nourafkan, R. %A Kotliar, G. %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 90 %P 125132 %8 Sep %U http://link.aps.org/doi/10.1103/PhysRevB.90.125132 %R 10.1103/PhysRevB.90.125132 %0 Journal Article %J Phys. Rev. B %D 2014 %T Phase diagram and Fermi liquid properties of the extended Hubbard model on the honeycomb lattice %A Wu, Wei %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 89 %P 205128 %8 May %U http://link.aps.org/doi/10.1103/PhysRevB.89.205128 %R 10.1103/PhysRevB.89.205128 %0 Journal Article %J Nano Letters %D 2014 %T Telegraphic noise in transport through colloidal quantum dots %A Lachance-Quirion, D. %A A.-M. S. Tremblay %A Lamarre, S.A. %A Méthot, V. %A Gingras, D. %A Camirand Lemyre, J. %A M Pioro-Ladrière %A Allen, C.N. %B Nano Letters %V 14 %P 882-887 %G eng %U http://www.scopus.com/inward/record.url?eid=2-s2.0-84894149742&partnerID=40&md5=5635c4b4bcbd83fb40a95f37de0b0fad %0 Journal Article %J Phys. Rev. B %D 2013 %T c-axis resistivity, pseudogap, superconductivity, and Widom line in doped Mott insulators %A Sordi, G. %A Sémon, P. %A Haule, K. %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 87 %P 041101 (R) %8 Jan %U http://link.aps.org/doi/10.1103/PhysRevB.87.041101 %R 10.1103/PhysRevB.87.041101 %0 Journal Article %J Phys. Rev. B %D 2013 %T Entropy, frustration, and large thermopower of doped Mott insulators on the fcc lattice %A Arsenault, Louis-François %A Shastry, B. Sriram %A Sémon, Patrick %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 87 %P 035126 %8 Jan %U http://link.aps.org/doi/10.1103/PhysRevB.87.035126 %R 10.1103/PhysRevB.87.035126 %0 Journal Article %J Phys. Rev. B %D 2013 %T Mott p-n junctions in layered materials %A Charlebois, M. %A Hassan, S. R. %A Karan, R. %A D. Sénéchal %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 87 %P 035137 %8 Jan %U http://link.aps.org/doi/10.1103/PhysRevB.87.035137 %R 10.1103/PhysRevB.87.035137 %0 Journal Article %J Phys. Rev. B %D 2013 %T Resilience of d-wave superconductivity to nearest-neighbor repulsion %A D. Sénéchal %A Day, A. G. R. %A Bouliane, V. %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 87 %P 075123 %8 Feb %U http://link.aps.org/doi/10.1103/PhysRevB.87.075123 %R 10.1103/PhysRevB.87.075123 %0 Book Section %B Emergent Phenomena in Correlated Matter Modeling and Simulation %D 2013 %T Strongly correlated superconductivity %A A.-M. S. Tremblay %E Pavarini, Eva %E Koch, Erik %E Schollwöck, Ulrich %K cluster dynamical mean-field theory %K Cuprates %K organic superconductors %K Strong correlations %K Superconductivity %B Emergent Phenomena in Correlated Matter Modeling and Simulation %I Verlag des Forschungszentrum %C Jülich %V 3 %U http://www.cond-mat.de/events/correl13/manuscripts/correl13.pdf %& 10 %0 Journal Article %J Phys. Rev. B %D 2013 %T Transport functions for hypercubic and Bethe lattices %A Arsenault, Louis-François %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 88 %P 205109 %8 Nov %U http://link.aps.org/doi/10.1103/PhysRevB.88.205109 %R 10.1103/PhysRevB.88.205109 %0 Journal Article %J Phys. Rev. B %D 2012 %T Benchmark of a modified iterated perturbation theory approach on the fcc lattice at strong coupling %A Arsenault, Louis-François %A Sémon, Patrick %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 86 %P 085133 %8 Aug %U http://link.aps.org/doi/10.1103/PhysRevB.86.085133 %R 10.1103/PhysRevB.86.085133 %0 Journal Article %J Phys. Rev. B %D 2012 %T Breakdown of Fermi liquid behavior at the (π,π)=2k_F spin-density wave quantum-critical point: The case of electron-doped cuprates %A Bergeron, Dominic %A Chowdhury, Debanjan %A Punk, Matthias %A Sachdev, Subir %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 86 %P 155123 %8 Oct %U http://link.aps.org/doi/10.1103/PhysRevB.86.155123 %R 10.1103/PhysRevB.86.155123 %0 Journal Article %J Phys. Rev. B (R) %D 2012 %T Importance of subleading corrections for the Mott critical point %A Sémon, Patrick %A A.-M. S. Tremblay %B Phys. Rev. B (R) %I American Physical Society %V 85 %P 201101 %8 May %U http://www.physique.usherbrooke.ca/pages/node/8015 %R 10.1103/PhysRevB.85.201101 %0 Journal Article %J Scientific Reports %D 2012 %T Pseudogap temperature as a Widom line in doped Mott insulators %A Sordi, G. %A Sémon, P. %A Haule, K. %A A.-M. S. Tremblay %B Scientific Reports %V 2, 547 %8 07/2012 %U http://www.nature.com/srep/2012/120731/srep00547/full/srep00547.html %9 Journal Article %& 547 %R 10.1038/srep00547 %0 Journal Article %J Phys. Rev. Lett. %D 2012 %T Strong Coupling Superconductivity, Pseudogap, and Mott Transition %A Sordi, G. %A Sémon, P. %A Haule, K. %A A.-M. S. Tremblay %B Phys. Rev. Lett. %I American Physical Society %V 108 %P 216401 %8 May %U http://link.aps.org/doi/10.1103/PhysRevLett.108.216401 %R 10.1103/PhysRevLett.108.216401 %0 Journal Article %J Physical Review B %D 2011 %T d-wave superconductivity on the checkerboard Hubbard model at weak and strong coupling %A Shiladitya Chakraborty %A D. Sénéchal %A A.-M. S. Tremblay %B Physical Review B %V 84 %P 054545/1--8 %8 2011 %& 054545 %0 Journal Article %J Physics in Canada, La physique au Canada %D 2011 %T Foreword - "Superconductivity: Advances and Prospects" %A A.-M. S. Tremblay %B Physics in Canada, La physique au Canada %V 67 %8 06/2011 %& 59 %0 Journal Article %J Physics in Canada, La physique au Canada %D 2011 %T High-Temperature Superconductivity from Short-Range Repulsion %A A.-M. S. Tremblay %B Physics in Canada, La physique au Canada %V 67 %P 105 %0 Magazine Article %D 2011 %T La supraconductivité en un clin d'oeil %A A.-M. S. Tremblay %B Physics in Canada - La physique au Canada %V 67 %P 61-64 %8 06/2011 %N 2 %0 Journal Article %J Phys. Rev. B %D 2011 %T Mott physics and first-order transition between two metals in the normal-state phase diagram of the two-dimensional Hubbard model %A Sordi, G. %A Haule, K. %A A.-M. S. Tremblay %B Phys. Rev. B %I American Physical Society %V 84 %P 075161 %8 Aug %R 10.1103/PhysRevB.84.075161 %0 Journal Article %J Physical Review B %D 2011 %T Optical and dc conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point including vertex corrections %A Bergeron, Dominic %A Hankevych, Vasyl %A Kyung, Bumsoo %A A.-M. S. Tremblay %B Physical Review B %I American Physical Society %V 84 %P 085128/1-35 %8 2011 %& 085128 %R 10.1103/PhysRevB.84.085128 %0 Magazine Article %D 2011 %T Préface- La supraconductivité: progrès et perspectives %A Louis Taillefer %E A.-M. S. Tremblay %B Physics in Canada - La physique au Canada %V 67 %P 59 %8 06/2011 %N 2 %0 Journal Article %J Physics in Canada, La physique au Canada %D 2011 %T Superconductivity in a Nutshell %A A.-M. S. Tremblay %B Physics in Canada, La physique au Canada %V 67 %P 65-68 %8 06/2011 %0 Book Section %B Theoretical Methods for Strongly Correlated Systems %D 2011 %T Two-Particle-Self-Consistent Approach for the Hubbard Model %A A.-M. S. Tremblay %E Ferdinando Mancini %E Adolfo Avella %B Theoretical Methods for Strongly Correlated Systems %S Springer Series in SOlid-State Sciences, Vol. 171 %V Springer Series %@ ISBN 978-3-642-21830-9 %U http://www.springer.com/materials/book/978-3-642-21830-9 %& 13 %0 Journal Article %J Physical Review B (Editor's choice) %D 2010 %T Dynamical electronic nematicity from Mott physics %A Okamoto, S. %A D. Sénéchal %A Civelli, M. %A A.-M. S. Tremblay %XVery large anisotropies in transport quantities have been observed in the presence of very small in-plane structural anisotropy in many strongly correlated electron materials. By studying the two-dimensional Hubbard model with dynamical-mean-field theory for clusters, we show that such large anisotropies can be induced without static stripe order if the interaction is large enough to yield a Mott transition. Anisotropy decreases at large frequency. The maximum effect on conductivity anisotropy occurs in the underdoped regime, as observed in high-temperature superconductors.

%B Physical Review B (Editor's choice) %V 82 %P 180511(R)/1-4 %8 2010 %G eng %0 Journal Article %J Physical Review Letters %D 2010 %T Finite Doping Signatures of the Mott Transition in the Two-Dimensional Hubbard Model %A Sordi, G. %A Haule, K. %A A.-M. S. Tremblay %XExperiments on layered materials call for a study of the influence of short-range spin correlations on the Mott transition. To this end, we solve the cellular dynamical mean-field equations for the Hubbard model on a plaquette with continuous-time quantum Monte Carlo calculations. The normal-state phase diagram as a function of temperature T, interaction strength U, and filling n reveals that upon increasing n towards the insulator, there is a surface of first-order transition between two metals at nonzero doping. For T above the critical end line there is a maximum in scattering rate.

%B Physical Review Letters %V 104 %P 226401/1-4 %8 2010 %G eng %0 Journal Article %J Physical Review B %D 2010 %T Generalized dc and ac Josephson effects in antiferromagnets and in antiferromagnetic d-wave superconductors %A Chasse, D. %A A.-M. S. Tremblay %XThe Josephson effect is generally described as Cooper-pair tunneling but it can also be understood in a more general context. The dc Josephson effect is the pseudo-Goldstone boson of two coupled systems with a broken continuous Abelian U(1) symmetry. Hence, an analog should exist for systems with broken continuous non-Abelian symmetries. To exhibit the generality of the phenomenon and make predictions from a realistic model, we study tunneling between antiferromagnets and also between antiferromagnetic d-wave superconductors. Performing a calculation analogous to that of Ambegaokar and Baratoff for the Josephson junction, we find an equilibrium current of the staggered magnetization through the junction that, in antiferromagnets, is proportional to s(L)xs(R), where s(L) and s(R) are the Neacuteel vectors on either sides of the junction. Microscopically, this effect exists because of the coherent tunneling of spin-one particle-hole pairs. In the presence of a magnetic field which is different on either sides of the junction, we find an analog of the ac Josephson effect where the angle between Neacuteel vectors depends on time. In the case of antiferromagnetic d-wave superconductors we predict that there is a contribution to the critical current that depends on the antiferromagnetic order and a contribution to the spin-critical current that depends on superconducting order. The latter contributions come from tunneling of the triplet Cooper pair that is necessarily present in the ground state of an antiferromagnetic d-wave superconductor. All these effects appear to leading order in the square of the tunneling matrix elements.

%B Physical Review B %V 81 %P 115102/1-9 %8 2010 %G eng %0 Journal Article %J Europhysics Letters %D 2009 %T First-order Mott transition at zero temperature in two dimensions: Variational plaquette study %A Balzer, M. %A B. Kyung %A D. Sénéchal %A A.-M. S. Tremblay %A Potthoff, M. %XThe nature of the metal-insulator Mott transition at zero temperature has been discussed for a number of years. Whether it occurs through a quantum critical point or through a first-order transition is expected to profoundly influence the nature of the finite-temperature phase diagram. In this paper, we study the zero temperature Mott transition in the two-dimensional Hubbard model on the square lattice with the variational cluster approximation. This takes into account the influence of antiferromagnetic short-range correlations. By contrast to single-site dynamical mean-field theory, the transition turns out to be first order even at zero temperature. Copyright (C) EPLA, 2009

%B Europhysics Letters %V 85 %P 17002/1-6 %8 2009 %G eng %0 Journal Article %J Physical Review B %D 2009 %T Low-energy theory of the t-t '-t ''-U Hubbard model at half-filling: Interaction strengths in cuprate superconductors and an effective spin-only description of La2CuO4 %A Delannoy, J. Y. P. %A Gingras, M. J. P. %A Holdsworth, P. C. W. %A A.-M. S. Tremblay %XSpin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many other types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band-structure calculations and photoemission experiments on these systems, we include second-and third-neighbor hopping parameters, t' and t", into the Hubbard Hamiltonian. A unitary transformation method is used to find systematically the effective Hamiltonian and any operator in the spin-only representation. The results include all closed four-hop electronic pathways in the canonical transformation. The method generates many ring exchange terms that play an important role in the comparison with experiments on La2CuO4. Performing a spin-wave analysis, we calculate the magnon dispersion as a function of U, t, t', and t". The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. [Phys. Rev. Lett. 86, 5377 (2001)] for La2CuO4. The ring exchange terms are found essential, in particular to determine the relative sign of t' and t", with the values found in good agreement with independent theoretical and experimental estimates for other members of the cuprate family. The zero-temperature sublattice magnetization is calculated using these parameters and also found to be in good agreement with the experimental value estimated by Lee et al. [Phys. Rev. B 60, 3643 (1999)]. We find a value of the interaction strength U similar or equal to 8t consistent with Mott insulating behavior.

%B Physical Review B %V 79 %P 235130/1-22 %8 2009 %G eng %0 Journal Article %J Physical Review B %D 2009 %T Mixed pairing symmetry in kappa-(BEDT-TTF)(2)X organic superconductors from ultrasonic velocity measurements %A Dion, M. %A Fournier, D. %A Poirier, M. %A Truong, K. D. %A A.-M. S. Tremblay %XDiscontinuities in elastic constants are detected at the superconducting transition of layered organic conductors kappa-(BEDT-TTF)(2)X by longitudinal and transverse ultrasonic velocity measurements. Symmetry arguments show that discontinuities in shear elastic constants can be explained in the orthorhombic compound only if the superconducting order parameter has a mixed character that can be of two types, either A(1g)+B-1g or B-2g+B-3g in the classification of irreducible representations of the orthorhombic point group D-2h. Consistency with other measurements suggests that the A(1g)+B-1g(d(xy)+d(z(x+y))) possibility is realized. Such clear symmetry-imposed signatures of mixed order parameters have not been observed in other superconducting compounds.

%B Physical Review B %V 80 %P 220511(R)/1-4 %8 2009 %G eng %0 Journal Article %J Physical Review B %D 2009 %T Pairing dynamics in strongly correlated superconductivity %A B. Kyung %A D. Sénéchal %A A.-M. S. Tremblay %XConfirmation of the phononic origin of Cooper pair formation in superconductors came with the demonstration that the interaction was retarded and that the corresponding energy scales were associated with phonons. Using cellular dynamical mean-field theory for the two-dimensional Hubbard model, we identify such retardation effects in d-wave pairing and associate the corresponding energy scales with short-range spin fluctuations. We find which frequencies are relevant for pairing as a function of interaction strength and doping and show that the disappearance of superconductivity on the overdoped side coincides with the disappearance of the low-energy feature in the antiferromagnetic fluctuations, as observed in neutron-scattering experiments.

%B Physical Review B %V 80 %P 205109/1-8 %8 2009 %G eng %0 Journal Article %J Physical Review B %D 2008 %T Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators %A Kancharla, S. S. %A B. Kyung %A D. Sénéchal %A Civelli, M. %A Capone, M. %A Kotliar, G. %A A.-M. S. Tremblay %XProximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step toward a quantitative theory of the competition between antiferromagnetism and d-wave superconductivity in the cuprates, we use cellular dynamical mean-field theory to compute zero-temperature properties of the two-dimensional square lattice Hubbard model. The d-wave order parameter is found to scale like the superexchange coupling J for on-site interaction U comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping, while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second neighbor hopping t', the zero-temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third neighbor hopping t '' improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping Vs T-c/T-c(max) phase diagram of the cuprates is universal. The calculated angle-resolved photoemission spectrum displays the observed electron-hole asymmetry. The tendency to homogeneous coexistence of the superconducting and antiferromagnetic order parameters is stronger than observed in most experiments but consistent with many theoretical results and with experiments in some layered high-temperature superconductors. Clearly, our calculations reproduce important features of d-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard Bardeen-Cooper-Schrieffer approach. At strong coupling, d-wave superconductivity and antiferromagnetism naturally appear as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.

%B Physical Review B %V 77 %P 184516/1-12 %8 2008 %G eng %0 Journal Article %J Physical Review B %D 2008 %T Competition between charge and spin order in the t-U-V extended Hubbard model on the triangular lattice %A Davoudi, B. %A Hassan, S. R. %A A.-M. S. Tremblay %XSeveral new classes of compounds can be modeled in first approximation by electrons on the triangular lattice that interact through on-site repulsion U as well as nearest-neighbor repulsion V. This extended Hubbard model on a triangular lattice has been studied mostly in the strong coupling limit for only a few types of instabilities. Using the extended two-particle self-consistent approach (ETPSC), that is valid at weak to intermediate coupling, we present an unbiased study of the density and interaction dependent crossover diagram for spin- and charge-density wave instabilities of the normal state at arbitrary wave vector. When U dominates over V and electron filling is large, instabilities are chiefly in the spin sector and are controlled mostly by Fermi surface properties. Increasing V eventually leads to charge instabilities. In the latter case, it is mostly the wave vector dependence of the vertex that determines the wave vector of the instability rather than Fermi surface properties. At small filling, nontrivial instabilities appear only beyond the weak coupling limit. There again, charge-density wave instabilities are favored over a wide range of dopings by large V at wave vectors corresponding to root(3) x root(3) superlattice in real space. Commensurate fillings do not play a special role for this instability. Increasing U leads to competition with ferromagnetism. At negative values of U or V, neglecting superconducting fluctuations, one finds that charge instabilities are favored. In general, the crossover diagram presents a rich variety of instabilities. We also show that thermal charge-density wave fluctuations in the renormalized-classical regime can open a pseudogap in the single-particle spectral weight, just as spin or superconducting fluctuations.

%B Physical Review B %V 77 %P 214408/1-11 %8 2008 %G eng %0 Journal Article %J Physical Review B %D 2008 %T Conditions for magnetically induced singlet d-wave superconductivity on the square lattice %A Hassan, S. R. %A Davoudi, B. %A B. Kyung %A A.-M. S. Tremblay %XIt is expected that at weak to intermediate coupling, d-wave superconductivity can be induced by antiferromagnetic fluctuations. However, one needs to clarify the role of Fermi surface topology, density of states, pseudogap, and wave vector of the magnetic fluctuations on the nature and strength of the induced d-wave state. To this end, we study the generalized phase diagram of the two-dimensional half-filled Hubbard model as a function of interaction strength U/t, frustration induced by second-order hopping t'/t, and temperature T/t. In experiment, U/t and t'/t can be controlled by pressure. We use the two-particle self-consistent approach, valid from weak to intermediate coupling. We first calculate as a function of t'/t and U/t the temperature and wave vector at which the spin response function begins to grow exponentially. d-wave superconductivity in a half-filled band can be induced by such magnetic fluctuations at weak to intermediate coupling, but only if they are near commensurate wave vectors and not too close to perfect nesting conditions where the pseudogap becomes detrimental to superconductivity. For given U/t, there is thus an optimal value of frustration t'/t where the superconducting T-c is maximum. The noninteracting density of states plays little role. The symmetry d(x2-y2) vs d(xy) of the superconducting order parameter depends on the wave vector of the underlying magnetic fluctuations in a way that can be understood qualitatively from simple arguments.

%B Physical Review B %V 77 %P 094501/1-9 %8 2008 %G eng %0 Journal Article %J Physical Review B %D 2008 %T Convexity of the self-energy functional in the variational cluster approximation %A Nevidomskyy, A. H. %A D. Sénéchal %A A.-M. S. Tremblay %XIn the variational cluster approximation (VCA) (or variational cluster perturbation theory), widely used to study the Hubbard model, a fundamental problem that renders variational solutions difficult in practice is its known lack of convexity at stationary points, i.e., the physical solutions can be saddle points rather than extrema of the self-energy functional. Here, we suggest two different approaches to construct a convex functional Omega[Sigma]. In the first approach, one can show analytically that in the approximation where the irreducible particle-hole vertex depends only on center of mass coordinates, the functional is convex away from phase transitions in the corresponding channel. Numerical tests on a tractable version of that functional show that convexity can be a nuisance when looking for instabilities both in the pairing and particle-hole channels. Therefore, an alternative phenomenological functional is proposed. Convexity is explicitly enforced only with respect to a restricted set of variables, such as the cluster chemical potential that is known to be otherwise problematic. Numerical tests show that our functional is convex at the physical solutions of VCA and allows second-order phase transitions in the pairing channel as well. This opens the way to the use of more efficient algorithms to find solutions of the VCA equations.

%B Physical Review B %V 77 %P 075105/1-12 %8 2008 %G eng %0 Journal Article %J Physical Review B %D 2008 %T Magnetism and d-wave superconductivity on the half-filled square lattice with frustration %A Nevidomskyy, A. H. %A Scheiber, C. %A D. Sénéchal %A A.-M. S. Tremblay %XThe role of frustration and interaction strength on the half-filled Hubbard model is studied on the square lattice with nearest- and next-nearest-neighbor hoppings t and t(') using the variational cluster approximation (VCA). At half-filling, we find two phases with long-range antiferromagnetic (AF) order: the usual Neel phase, stable at small frustration t(')/t, and the so-called collinear (or superantiferromagnet) phase with ordering wave vector (pi,0) or (0,pi), stable for large frustration. These are separated by a phase with no detectable long-range magnetic order. We also find the d-wave superconducting (SC) phase (d(x)(2)-y(2)), which is favored by frustration if it is not too large. Intriguingly, there is a broad region of coexistence where both AF and SC order parameters have nonzero values. In addition, the physics of the metal-insulator transition in the normal state is analyzed. The results obtained with the help of the VCA method are compared with the large-U expansion of the Hubbard model and known results for the frustrated J(1)-J(2) Heisenberg model. These results are relevant for pressure studies of undoped parents of the high-temperature superconductors: we predict that an insulator to d-wave SC transition may appear under pressure.

%B Physical Review B %V 77 %P 064427/1-13 %8 2008 %G eng %0 Journal Article %J Europhysics Letters %D 2008 %T Scaling and commensurate-incommensurate crossover for the d=2 %A Roy, S. %A A.-M. S. Tremblay %X{Quantum critical points exist at zero temperature, yet, experimentally their influence seems to extend over a large part of the phase diagram of systems such as heavy-fermion compounds and high-temperature superconductors. Theoretically, however, it is generally not known over what range of parameters the physics is governed by the quantum critical point. We answer this question for the spin-density wave to Fermi-liquid quantum critical point in the two-dimensional Hubbard model. This problem is in the d = 2

%B Europhysics Letters %V 84 %P 37013/1-6 %8 2008 %G eng %0 Journal Article %J Physical Review B %D 2007 %T Interaction-induced adiabatic cooling for antiferromagnetism in optical lattices %A Dare, A. M. %A Raymond, L. %A Albinet, G. %A A.-M. S. Tremblay %XIn the experimental context of cold-fermion optical lattices, we discuss the possibilities to approach the pseudogap or ordered phases by manipulating the scattering length or the strength of the laser-induced lattice potential. Using the two-particle self-consistent approach, as well as quantum Monte Carlo simulations, we provide isentropic curves for the two- and three-dimensional Hubbard models at half-filling. These quantitative results are important for practical attempts to reach the ordered antiferromagnetic phase in experiments on optical lattices of two-component fermions. We find that adiabatically turning on the interaction in two dimensions to cool the system is not very effective. In three dimensions, adiabatic cooling to the antiferromagnetic phase can be achieved in such a manner, although the cooling efficiency is not as high as initially suggested by dynamical mean-field theory. Adiabatic cooling by turning off the repulsion beginning at strong coupling is possible in certain cases.

%B Physical Review B %V 76 %P 064492/1-10 %8 2007 %G eng %0 Journal Article %J Physical Review B %D 2007 %T Non-perturbative treatment of charge and spin fluctuations in the two-dimensional extended Hubbard model: Extended two-particle self-consistent approach %A Davoudi, B. %A A.-M. S. Tremblay %XWe study the spin and charge fluctuations of the extended Hubbard model with on-site interaction U and first neighbor interaction V on the two-dimensional square lattice in the weak to intermediate coupling regime. We propose an extension of the two-particle self-consistent approximation that includes the effect of functional derivatives of the pair-correlation functions on irreducible spin and charge vertices. These functional derivatives were ignored in our previous work. We evaluate them assuming particle-hole symmetry. The resulting theory satisfies conservation laws and the Mermin-Wagner theorem. Our current results are in much better agreement with benchmark quantum Monte Carlo results. This theory allows us to reliably determine the crossover temperatures toward renormalized-classical regimes, and hence, the dominant instability as a function of U and V. We have considered fillings n=1 and n=0.75. Either spin or charge fluctuations can dominate. The wave vector is self-determined by the approach.

%B Physical Review B %V 76 %P 085115/1-12 %8 2007 %G eng %0 Journal Article %J Physical Review B %D 2007 %T Supersolidity, entropy, and frustration: t-t '-V model of hard-core bosons on the triangular lattice %A Hassan, S. R. %A de Medici, L. %A A.-M. S. Tremblay %XWe study the properties of t-t(')-V model of hard-core bosons on the triangular lattice that can be realized in optical lattices. By mapping to the spin-1/2 XXZ model in a field, we determine the phase diagram of the t-V model where the supersolid characterized by the ordering pattern (x,x,-2x(')) ("ferrimagnetic" or SS A) is a ground state for chemical potential mu>3V. By turning on either temperature or t(') at half filling (mu=3V), we find a first order transition from SS A to the elusive supersolid characterized by the (x,-x,0) ordering pattern ("antiferromagnetic" or SS C). In addition, we find a large region where a superfluid phase becomes a solid upon increasing temperature at fixed chemical potential. This is an analog of the Pomeranchuk effect driven by the large entropic effects associated with geometric frustration on the triangular lattice.

%B Physical Review B %V 76 %P 144420/1-4 %8 2007 %G eng %0 Journal Article %J Physical Review Letters %D 2006 %T Comment on "Spin correlations in the paramagnetic phase and ring exchange in La2CuO4" %A Raymond, L. %A Albinet, G. %A A.-M. S. Tremblay %B Physical Review Letters %V 97 %P 049701 %8 2006 %G eng %0 Journal Article %J Physical Review Letters %D 2006 %T Mott transition, antiferromagnetism, and d-wave superconductivity in two-dimensional organic conductors %A B. Kyung %A A.-M. S. Tremblay %XWe study the Mott transition, antiferromagnetism, and superconductivity in layered organic conductors using the cellular dynamical mean-field theory for the frustrated Hubbard model. A d-wave superconducting phase appears between an antiferromagnetic insulator and a metal for t(')/t=0.3-0.7 or between a nonmagnetic Mott insulator (spin liquid) and a metal for t(')/t >= 0.8, in agreement with experiments on layered organic conductors including kappa-(ET)(2)Cu-2(CN)(3). These phases are separated by a strong first-order transition. The phase diagram gives much insight into the mechanism for d-wave superconductivity. Two predictions are made.

%B Physical Review Letters %V 97 %P 046402/1-4 %8 2006 %G eng %0 Journal Article %J Physical Review B %D 2006 %T Nearest-neighbor repulsion and competing charge and spin order in the extended Hubbard model %A Davoudi, B. %A A.-M. S. Tremblay %XWe generalize the two-particle self-consistent approach (TPSC) to study the extended Hubbard model, where nearest-neighbor interaction is present in addition to the usual local screened interaction. Similarities and differences between the TPSC approach and the Singwi, Tosi, Land, Sjolander (STLS) approximation for the electron gas are discussed. The accuracy of our extension of TPSC is assessed by comparisons with Quantum Monte Carlo calculations of Y. Zhang and J. Callaway [Phys. Rev. B 39, 9397 (1989)]. We quantify how a positive off-site interaction enhances staggered charge fluctuations and reduces staggered magnetic order.

%B Physical Review B %V 74 %P 035113/1-15 %8 2006 %G eng %0 Journal Article %J Physical Review B %D 2006 %T Potential-energy-driven (BCS) to kinetic-energy-driven (BEC) pairing in the two-dimensional attractive Hubbard model: Cellular dynamical mean-field theory %A B. Kyung %A Georges, A. %A A.-M. S. Tremblay %XThe BCS-BEC crossover within the two-dimensional attractive Hubbard model is studied by using the Cellular Dynamical Mean-Field Theory, both in the normal and superconducting ground states. Short-range spatial correlations incorporated in this theory remove the normal-state quasiparticle peak and the first-order transition found in the Dynamical Mean-Field Theory, rendering the normal state crossover smooth. For U smaller than the bandwidth, pairing is driven by the potential energy, while in the opposite case it is driven by the kinetic energy, resembling a recent optical conductivity experiment in cuprates. Phase coherence leads to the appearance of a collective Bogoliubov mode in the density-density correlation function and to the sharpening of the spectral function. (c) 2006 American Institute of Physics.

%B Physical Review B %V 74 %P 0245501/1-5 %8 2006 %G eng %0 Journal Article %J Low Temperature Physics %D 2006 %T Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards a quantitative theory %A A.-M. S. Tremblay %A B. Kyung %A D. Sénéchal %XThis is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole- and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments had been predicted by theory before it was observed experimentally. Additional experimental confirmation would be useful. The theoretical methods that are surveyed include mostly the two-particle self-consistent approach, variational cluster perturbation theory (or variational cluster approximation), and cellular dynamical mean-field theory. (c) 2006 American Institute of Physics.

%B Low Temperature Physics %V 32 %P 424–451 %G eng %0 Journal Article %J Physical Review B %D 2006 %T Pseudogap induced by short-range spin correlations in a doped Mott insulator %A B. Kyung %A Kancharla, S. S. %A D. Sénéchal %A A.-M. S. Tremblay %A Civelli, M. %A Kotliar, G. %XWe study the evolution of a Mott-Hubbard insulator into a correlated metal upon doping in the two-dimensional Hubbard model using the cellular dynamical mean-field theory. Short-range spin correlations create two additional bands apart from the familiar Hubbard bands in the spectral function. Even a tiny doping into this insulator causes a jump of the Fermi energy to one of these additional bands and an immediate momentum-dependent suppression of the spectral weight at this Fermi energy. The pseudogap is closely tied to the existence of these bands. This suggests a strong-coupling mechanism that arises from short-range spin correlations and large scattering rates for the pseudogap phenomenon seen in several cuprates.

%B Physical Review B %V 73 %P 1651114/1-6 %8 2006 %G eng %0 Journal Article %J Physical Review B %D 2006 %T Quantum Monte Carlo study of strongly correlated electrons: Cellular dynamical mean-field theory %A B. Kyung %A Kotliar, G. %A A.-M. S. Tremblay %XWe study the Hubbard model using the cellular dynamical mean-field theory (CDMFT) with quantum Monte Carlo (QMC) simulations. We present the algorithmic details of CDMFT with the Hirsch-Fye QMC method for the solution of the self-consistently embedded quantum cluster problem. We use the one- and two-dimensional half filled Hubbard model to gauge the performance of CDMFT+QMC particularly for small clusters by comparing with the exact results and also with other quantum cluster methods. We calculate single-particle Green's functions and self-energies on small clusters to study their size dependence in one and two dimensions. It is shown that in one dimension, CDMFT with two sites in the cluster is already able to describe with high accuracy the evolution of the density as a function of the chemical potential and the compressibility divergence at the Mott transition, in good agreement with the exact Bethe ansatz result. With increasing U the result on small clusters rapidly approaches that of the infinite size cluster. Large scattering rate and a positive slope in the real part of the self-energy in one dimension suggest that the system is a non-Fermi liquid for all the parameters studied here. In two dimensions, at intermediate to strong coupling, even the smallest cluster (N-c=2x2) accounts for more than 95% of the correlation effect of the infinite-size cluster in the single particle spectrum, suggesting that some of the important problems in strongly correlated electron systems may be studied highly accurately with a reasonable computational effort. Finally, as an application that is sensitive to details of correlations, we show that CDMFT+QMC can describe spin-charge separated Luttinger liquid physics in one dimension. The spinon and holon branches appear only for sufficiently large system sizes.

%B Physical Review B %V 73 %P 205106/1-13 %8 2006 %G eng %0 Journal Article %J Journal of Physics and Chemistry of Solids %D 2006 %T Strong- and weak-coupling mechanisms for pseudogap in electron-doped cuprates %A Hankevych, V. %A B. Kyung %A Dare, A. M. %A D. Sénéchal %A A.-M. S. Tremblay %XUsing the two-particle self-consistent approach and cluster perturbation theory for the two-dimensional t-t'-t"-U Hubbard model, we discuss weak- and strong-coupling mechanisms for the pseudogap observed in recent angle resolved photoemission spectroscopy on electron-doped cuprates. In the case of the strong-coupling mechanism, which is more relevant near half-filling, the pseudogap can be mainly driven by short-range correlations near the Mott insulator. In the vicinity of optimal doping, where weak-coupling physics is more relevant, large antiferromagnetic correlation lengths, seen in neutron measurements, are the origin of the pseudogap. The t-J model is not applicable in the latter case. (c) 2006 Elsevier Ltd. All rights reserved.

%B Journal of Physics and Chemistry of Solids %V 67 %P 189–192 %G eng %0 Journal Article %J Physical Review Letters %D 2005 %T Competition between Antiferromagnetism and Superconductivity in High-$T_c$ Cuprates %A D. Sénéchal %A P.-L. Lavertu %A M.-A. Marois %A A.-M. S. Tremblay %K Sans titre %B Physical Review Letters %V 94 %P 156404/1-4 %8 2005 %G eng %& 156404 %0 Journal Article %J Physical Review B %D 2005 %T Effect of superconducting fluctuations on ultrasound in an unconventional superconductor %A Mar'enko, M. S. %A C Bourbonnais %A A.-M. S. Tremblay %XWe study the renormalization of sound attenuation and sound velocity by fluctuation Cooper pairs in layered superconductors. We consider the influence of s- and d-wave symmetry of the fluctuating order parameter on both longitudinal and transverse phonon modes. We show that both unconventional order parameter symmetry and transverse sound polarization suppress the Aslamazov-Larkin and Maki-Thompson terms, while the density-of-states contribution is the least affected. The combination of these effects can change the sign of the overall fluctuation corrections above T-c. We also compare the results obtained using the Ginzburg-Landau formalism with a microscopic derivation of the fluctuation corrections to the sound velocity in both s- and d-wave superconductors. These calculations are motivated by ongoing ultrasound measurements in organic superconductors.

%B Physical Review B %V 72 %P 024508/1-13 %8 2005 %G eng %0 Journal Article %J Physical Review B %D 2005 %T Neel order, ring exchange, and charge fluctuations in the half-filled Hubbard model %A Delannoy, J. Y. P. %A Gingras, M. J. P. %A Holdsworth, P. C. W. %A A.-M. S. Tremblay %XWe investigate the ground state properties of the two-dimensional half-filled one band Hubbard model in the strong (large-U) to intermediate coupling limit (i.e., away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order t(t/U)(3). We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuations as t/U is increased from the t/U -> 0 Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an S=1/2 antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of t/U, despite the fact that the moment of the spin Hamiltonian, which depends on transverse spin fluctuations only, in an increasing function of t/U. We also comment on quantitative aspects of the t/U and 1/S expansions.

%B Physical Review B %V 72 %P 115114/1-8 %8 2005 %G eng %0 Journal Article %J Physical Review B %D 2004 %T Higher order corrections to effective low-energy theories for strongly correlated electron systems %A Chernyshev, A. L. %A Galanakis, D. %A Phillips, P. %A Rozhkov, A. V. %A A.-M. S. Tremblay %XThree well-known perturbative approaches to deriving low-energy effective theories, the degenerate Brillouin-Wigner perturbation theory (projection method), the canonical transformation, and the resolvent methods, are compared. We use the Hubbard model as an example to show how, to fourth order in hopping t, all methods lead to the same effective theory, namely the t-J model with ring exchange and various correlated hoppings. We emphasize subtle technical difficulties that make such a derivation less trivial to carry out for orders higher than second. We also show that in higher orders, different approaches can lead to seemingly different forms for the low-energy Hamiltonian. All of these forms are equivalent since they are connected by an additional unitary transformation whose generator is given explicitly. The importance of transforming the operators is emphasized and the equivalence of their transformed structure within the different approaches is also demonstrated.

%B Physical Review B %V 70 %P 235111/1-12 %8 2004 %G eng %0 Journal Article %J Physical Review Letters %D 2004 %T Hot spots and pseudogaps for hole- and electron-doped high-temperature superconductors %A D. Sénéchal %A A.-M. S. Tremblay %XUsing cluster perturbation theory, it is shown that the spectral weight and pseudogap observed at the Fermi energy in recent angle resolved photoemission spectroscopy of both electron- and hole-doped high-temperature superconductors find their natural explanation within the t-t(')-t('')-U Hubbard model in two dimensions. The value of the interaction U needed to explain the experiments for electron-doped systems at optimal doping is in the weak to intermediate coupling regime where the t-J model is inappropriate. At strong coupling, short-range correlations suffice to create a pseudogap, but at weak-coupling long correlation lengths associated with the antiferromagnetic wave vector are necessary.

%B Physical Review Letters %V 92 %P 126401/1-4 %8 2004 %G eng %0 Journal Article %J Physical Review Letters %D 2004 %T Pseudogap and spin fluctuations in the normal state of the electron-doped cuprates %A B. Kyung %A Hankevych, V. %A Dare, A. M. %A A.-M. S. Tremblay %XWe present reliable many-body calculations for the t-t(')-t('')-U Hubbard model that explain in detail the results of recent angle-resolved photoemission experiments on electron-doped high-temperature superconductors. The origin of the pseudogap is traced to two-dimensional antiferromagnetic spin fluctuations whose calculated temperature-dependent correlation length also agrees with recent neutron scattering measurements. We make specific predictions for photoemission, for neutron scattering, and for the phase diagram.

%B Physical Review Letters %V 93 %P 147994/1-4 %8 2004 %G eng %0 Conference Proceedings %B Spectroscopies in Novel Superconductors %D 2004 %T Strong- and weak-coupling mechanisms for pseudogap in electron-doped cuprates %A Hankevych, Vasyl %A Kyung, Bumsoo %A Daré, A.-M. %A D. Sénéchal %A A.-M. S. Tremblay %B Spectroscopies in Novel Superconductors %V Journal of Physics and Chemistry of Solids : 67 %P 189-192 %8 2006 %0 Journal Article %J Physical Review B %D 2004 %T Superconducting fluctuation corrections to ultrasound attenuation in layered superconductors %A Mar'enko, M. S. %A C Bourbonnais %A A.-M. S. Tremblay %XWe consider the temperature dependence of the sound attenuation and sound velocity in layered impure metals due to s-wave superconducting fluctuations of the order parameter above the critical temperature. We obtain the dependence on material properties of these fluctuation corrections in the hydrodynamic limit, where the electron mean free path l is much smaller than the wavelength of sound and where the electron collision rate tau(-1) is much larger than the sound frequency. For longitudinal sound propagating perpendicular to the layers, the open Fermi surface condition leads to a suppression of the divergent contributions to leading order, in contrast with the case of paraconductivity. The leading temperature dependent corrections, given by the Aslamazov-Larkin, Maki-Thompson and density-of-states terms, remain finite as T–>T-c. Nevertheless, the sensitivity of new ultrasonic experiments on layered organic conductors should make these fluctuations effects measurable.

%B Physical Review B %V 69 %P 224503-1-224503-12 %G eng %0 Book Section %D 2004 %T Theoretical Methods For Strongly Correlated Electrons %A S. Allen %A A.-M. S. Tremblay %A Vilk, Y.M. %E D. Sénéchal %E A.-M. S. Tremblay %E C Bourbonnais %XThe conserving approximation scheme to many-body problems was developed by Kadanoff and Baym using the functional-derivative approach. Another approach for the Hubbard model also satisfies conservation laws, but in addition it satisfies the Pauli principle and a number of sum rules. A concise formal derivation of that approach, using functional derivatives, is given in this conference paper to highlight formal analogies and differences with conserving approximations.

%I Springer %P 341–355 %G eng %& Conserving approximations vs. two-particle self-consistent approach %0 Journal Article %J Physical Review B %D 2003 %T Antiferromagnetic fluctuations and d-wave superconductivity in electron-doped high-temperature superconductors %A B. Kyung %A J.S. Landry %A A.-M. S. Tremblay %XWe show that, at weak to intermediate coupling, antiferromagnetic fluctuations enhance d-wave pairing correlations until, as one moves closer to half-filling, the antiferromagnetically induced pseudogap begins to suppress the tendency to superconductivity. The accuracy of our approach is gauged by detailed comparisons with quantum Monte Carlo simulations. The negative pressure dependence of T-c and the existence of photoemission hot spots in electron-doped cuprate superconductors find their natural explanation within this approach.

%B Physical Review B %V 68 %P 174502/1-5 %8 2003 %G eng %0 Journal Article %J Phys. Rev. Lett %D 2003 %T Comment on 'Absence of a Slater Transition in the Two-Dimensional Hubbard Model' %A B. Kyung %A J.S. Landry %A Poulin, D. %A A.-M. S. Tremblay %K Condensed matter %K Many-Body %K Simulation %X{In a recent paper, Physical Review Letters 87, 167010/1-4 (2001), Moukouri and Jarrell presented evidence that in the two-dimensional (d=2) Hubbard model at half-filling there is a metal-insulator transition (MIT) at finite temperature even in weak coupling. While we agree with the numerical results of that paper, we arrive at different conclusions: The apparent gap at finite-temperature can be understood, at weak-coupling, as a crossover phenomenon involving large (but not infinite) antiferromagnetic (AFM) correlation length. Phase-space effects on the self-energy in d=2 are crucial, as are the ratio between AFM correlation length and single-particle thermal de Broglie wavelength. In weak coupling

%B Phys. Rev. Lett %V 90 %P 099702 %G eng %0 Journal Article %J Physical Review A %D 2003 %T Effect of noise on geometric logic gates for quantum computation %A Blais, A. %A A.-M. S. Tremblay %XWe introduce the nonadiabatic, or Aharonov-Anandan, geometric phase as a tool for quantum computation and show how this phase on one qubit can be monitored by a second qubit without any dynamical contribution. We also discuss how this geometric phase could be implemented with superconducting charge qubits. While the nonadiabatic geometric phase may circumvent many of the drawbacks related to the adiabatic (Berry) version of geometric gates, we show that the effect of fluctuations of the control parameters on nonadiabatic phase gates is more severe than for the standard dynamic gates. Similarly, fluctuations also affect to a greater extent quantum gates that use the Berry phase instead of the dynamic phase.

%B Physical Review A %V 67 %P 012308/1-012308/7 %G eng %0 Book %B CRM Series in Mathematical Physics %D 2003 %T Theoretical Methods for Strongly Correlated Electrons %A D. Sénéchal %A A.-M. S. Tremblay %A C Bourbonnais %B CRM Series in Mathematical Physics %I 2003 %C New York %V Springer %P 361 %0 Journal Article %J Physical Review B %D 2003 %T Weak ferromagnetism and other instabilities of the two-dimensional t-t(') Hubbard model at van Hove fillings %A Hankevych, V. %A B. Kyung %A A.-M. S. Tremblay %XWe investigate magnetic and superconducting instabilities of the two-dimensional t-t(') Hubbard model on a square lattice at van Hove densities from weak to intermediate coupling by means of the two-particle self-consistent approach. We find that as the next-nearest-neighbor hopping \t(')\ increases from zero, the leading instability is towards an incommensurate spin-density wave whose wave vector moves slowly away from (pi,pi). For intermediate values of \t(')\, the leading instability is towards d(x)(2)-y(2)-wave superconductivity. For larger \t(')\>0.33t, there are signs of a crossover to ferromagnetism at extremely low temperatures. The suppression of the crossover temperature is driven by Kanamori screening that strongly renormalizes the effective interaction and also causes the crossover temperature to depend only weakly on t('). Electronic self-energy effects for large \t(')\ lead to considerable reduction of the zero-energy single-particle spectral weight beginning at temperatures as high as Tless than or similar to0.1t, an effect that may be detrimental to the existence of a ferromagnetic ground state at weak coupling.

%B Physical Review B %V 68 %P 2114405/1-11 %8 2003 %G eng %0 Conference Proceedings %B 17th annual international symposium on High Performance Computing Systems and Applications and the OSCAR Symposium %D 2003 %T What is the Hamiltonian for parent high-temperature superconductors? %A Alexis Gagné-Lebrun %A A.-M. S. Tremblay %E D. Sénéchal %B 17th annual international symposium on High Performance Computing Systems and Applications and the OSCAR Symposium %S NRC-CNRC Research Press, Ottawa %I NRC-CNRC Research Press, Ottawa %V Proceedings of the 17th annual international symposium on High Performance Computing Systems and Applications and the OSCAR Symp %P 71-77 %8 2003 %0 Journal Article %J arXiv %D 2002 %T Phenomenological description of competing antiferromagnetism and d-wave superconductivity in high $T_c$ cuprates %A B. Kyung %A A.-M. S. Tremblay %B arXiv %U http://lanl.arxiv.org/abs/cond-mat/0204500 %9 preprint %! Phenomenological description of competing antiferromagnetism and d-wave superconductivity in high $T_{c}$ cuprates %0 Book Section %B Theoretical Methods for Strongly Correlated Electrons %D 2001 %T Conserving approximations vs Two-Particle Self-Consistent Approach %A S. Allen %A A.-M. S. Tremblay %A Vilk, Y.M. %E D. Sénéchal %E A.-M. S. Tremblay %E C Bourbonnais %B Theoretical Methods for Strongly Correlated Electrons %S CRM Series in Mathematical Physics %I 2003 %V CRM Series in Mathematical Physics %P 341-355 %& 8 %0 Journal Article %J Physical Review B %D 2001 %T Nonperturbative approach to the attractive Hubbard model %A S. Allen %A A.-M. S. Tremblay %XA nonperturbative approach to the single-band attractive Hubbard model is presented in the general context of functional-derivative approaches to many-body theories. As in previous work on the repulsive model, the first step is bused on a local-field-type ansatz, on enforcement of the Pauli principle and a number of crucial sumrules. The Mermin-Wagner theorem in two dimensions is automatically satisfied. At this level, two-particle self-consistency has been achieved. In the second step of the approximation, an improved expression for the self-energy is obtained by using the results of the first step in an exact expression for the self-energy, where the high- and low-frequency behaviors appear separately. The result is a cooperon-like formula. The required vertex corrections are included in this self-energy expression, as required by the absence of a Migdal theorem for this problem. Other approaches to the attractive Hubbard model are critically compared. Physical consequences of the present approach and agreement with Monte Carlo simulations are demonstrated in the accompanying paper (following this one).

%B Physical Review B %V 64 %P art. no.–075115 %G eng %0 Journal Article %J Physical Review B %D 2001 %T Pairing fluctuations and pseudogaps in the attractive Hubbard model %A B. Kyung %A S. Allen %A A.-M. S. Tremblay %XThe two-dimensional attractive Hubbard model is studied in the weak-to-intermediate-coupling regime by employing a nonperturbative approach. It is shown that this approach is in quantitative agreement with Monte Carlo calculations for both single-particle and two-particle quantities. Both the density of states and the single-particle spectral weight show a pseudogap at the Fermi energy below some characteristic temperature T*, also in good agreement with quantum Monte Carlo calculations. The pseudogap is caused by critical pairing fluctuations in the low-temperature renormalized classical regime ((h) over bar omega

%B Physical Review B %V 64 %P art. no.–075116 %G eng %0 Journal Article %J Physical Review B %D 2000 %T Many-body theory versus simulations for the pseudogap in the Hubbard model %A Moukouri, S. %A S. Allen %A F. Lemay %A B. Kyung %A Poulin, D. %A Vilk, Y.M. %A A.-M. S. Tremblay %K Condensed matter %K Many-Body %K Simulation %XThe opening of a critical-fluctuation-induced pseudogap (or precursor pseudogap) in the one-particle spectral weight of the half-filled two-dimensional Hubbard model is discussed. This pseudogap, appearing in our Monte Carlo simulations, may be obtained from many-body techniques that use Green functions and vertex corrections that are at the same level of approximation. Self-consistent theories of the Eliashberg type (such as the fluctuation exchange approximation) use renormalized Green functions and bare vertices in a context where there is no Migdal theorem. They do not find the pseudogap, in quantitative and qualitative disagreement with simulations, suggesting these methods are inadequate for this problem. Differences between precursor pseudogaps and strong-coupling pseudogaps are also discussed.

%B Physical Review B %V 61 %P 7887–7892 %G eng %0 Journal Article %J Physics in Canada/La physique au Canada %D 2000 %T Strong correlations in low dimensional conductors: What are they and where are the challenges? %A A.-M. S. Tremblay %A C Bourbonnais %A D. Sénéchal %K Sans titre %B Physics in Canada/La physique au Canada %P 229 %8 Sept./Oct. %G eng %0 Journal Article %J European Physical Journal B %D 2000 %T Strong-coupling perturbation theory of the Hubbard model %A Pairault, S. %A D. Sénéchal %A A.-M. S. Tremblay %K Sans titre %XThe strong-coupling perturbation theory of the Hubbard model is presented and carried out tu order (t/U)(5) for the one-particle Green function In arbitrary dimension. The spectral weight A(k,omega) is expressed as a Jacobi continued fraction and compared with new Monte-Carlo data of the one-dimensional, half-filled Hubbard model. Different regimes (insulator, conductor and short-range antiferromagnet) are identified in the temperature-hopping integral (T, t) plane. This work completes a first paper on the subject (Phys. Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules and higher-order results. In addition, the non half-filled case, infinite resummations of diagrams and the double occupancy are discussed. Various tests: of the method are also presented.

%B European Physical Journal B %V 16 %P 85–105 %G eng %0 Conference Proceedings %B Mathématiques, enseignement des mathématiques: L'apport du XXe siècle %D 1999 %T Mathématiques, physique et technologies au XXe siècle %A A.-M. S. Tremblay %B Mathématiques, enseignement des mathématiques: L'apport du XXe siècle %I Les éditions du griffon d'argile, Sainte-Foy %C Sherbrooke %V Actes du 42e congrès annuel de l'Association mathématique du Québec %P 179-193 %8 2000 %@ 9782894431269 %0 Journal Article %J Physical Review Letters %D 1999 %T Role of symmetry and dimension in pseudogap phenomena %A S. Allen %A Touchette, H. %A Moukouri, S. %A Vilk, Y.M. %A A.-M. S. Tremblay %XThe attractive Hubbard model in d = 2 Ts studied through Monte Carlo simulations at intermediate coupling. There is a crossover temperature T-X where a pseudogap appears with concomitant precursors of Bogoliubov quasiparticles that are not local pairs. The pseudogap in A(k(F), omega) occurs in the renormalized classical regime when the correlation length is larger than the direction-dependent thermal de Broglie wavelength, xi(th) = (h) over bar nu(F)(k)/k(B)T. The ratio T-X/T-c for the pseudogap may be made arbitrarily large when the system is close to a point where the order parameter has SO(n) symmetry with n > 2. This is relevant in the context of SO(5) theories of high T-c but has more general applicability.

%B Physical Review Letters %V 83 %P 4128–4131 %G eng %0 Journal Article %J European Physical Journal B %D 1999 %T Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects %A Nelisse, H. %A C Bourbonnais %A Touchette, H. %A Vilk, Y.M. %A A.-M. S. Tremblay %XThe temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several methods. At low temperature, the renormalization group reveals that the Luttinger liquid spin susceptibility chi (T) approaches zero temperature with an infinite slope in striking contrast with the Fermi liquid result and with the behavior of the compressibility in the absence of umklapp scattering. This effect comes from the leading marginally irrelevant operator, in analogy with the Heisenberg spin 1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher temperature reveal that non-logarithmic terms are important in that regime. These contributions are evaluated from an effective interaction that includes the same set of diagrams as those that give the leading logarithmic terms in the renormalization group approach. Comments on the third law of thermodynamics as well as reasons for the failure of approaches that work in higher dimensions are given.

%B European Physical Journal B %V 12 %P 351–365 %G eng %0 Journal Article %J Journal of Physics and Chemistry of Solids %D 1998 %T Attractive Hubbard model and single-particle pseudogap caused by classical pairing fluctuations in two-dimensions %A Vilk, Y.M. %A S. Allen %A Touchette, H. %A Moukouri, S. %A Chen, L. %A A.-M. S. Tremblay %XIt is shown that in the two-dimensional attractive Hubbard model, the mean-field phase transition is replaced by a renormalized classical regime of fluctuations where a pseudogap opens up in the single-particle spectral weight. It is argued that this pseudogap and precursors of the ordered state quasiparticles can occur only in strongly anisotropic quasi-two-dimensional materials. This precursor phenomenon differs from preformed local pairs. Further, while critical antiferromagnetic fluctuations would also lead to a pseudogap in the repulsive model, there are some important differences with thr superconducting case. (C) 1998 Elsevier Science Ltd. All rights reserved.

%B Journal of Physics and Chemistry of Solids %V 59 %P 1873–1875 %G eng %0 Journal Article %J Physical Review Letters %D 1998 %T Strong-coupling expansion for the Hubbard model %A Pairault, S. %A D. Sénéchal %A A.-M. S. Tremblay %XA strong-coupling expansion for models of correlated electrons in any dimension is presented. The method is applied to the Hubbard model in d dimensions and compared with numerical results in d = 1. Third order expansion of the Green's function suffices to exhibit both the Mott metal-insulator transition and a low-temperature regime where antiferromagnetic correlations are strong. It is predicted that some of the weak photoemission signals observed in one-dimensional systems such as SrCuO2 should become stronger as temperature increases away from the spin-charge separated state.

%B Physical Review Letters %V 80 %P 5389–5392 %G eng %0 Journal Article %J Journal De Physique I %D 1997 %T Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap %A Vilk, Y.M. %A A.-M. S. Tremblay %XA new approach to the single-band Hubbard model is described in the general context of many-body theories. It is based on enforcing conservation laws, the Pauli principle and a number of crucial sum-rules. More specifically, spin and charge susceptibilities are expressed, in a conserving approximation, as a function of two irreducible vertices whose values are found by imposing the local Pauli principle [n(up arrow)(2)] = [n(up arrow)] as well as the local-moment sum-rule ana consistency with the equations of motion in a local-field approximation. The Mermin-Wagner theorem in two dimensions is automatically satisfied. The effect of collective modes on single-particle properties is then obtained by a paramagnon-like formula that is consistent with the two-particle properties in the sense that the potential energy obtained from Tr Sigma G is identical to that obtained using the fluctuation-dissipation theorem for susceptibilities. Since there is no Migdal theorem controlling the effect of spin and charge fluctuations on the self-energy, the required vertex corrections are included. It is shown that the theory is in quantitative agreement with Monte Carlo simulations for both single-particle and two-particle properties. The theory predicts a magnetic phase diagram where magnetic order persists away from half-filling but where ferromagnetism is completely suppressed. Both quantum-critical and renormalized-classical behavior can occur in certain parameter ranges. It is shown that in the renormalized classical regime, spin fluctuations lead to precursors of antiferromagnetic bands (shadow bands) and to the destruction of the Fermi-liquid quasiparticles in a wide temperature range above the zero-temperature phase transition. The upper critical dimension for this phenomenon is three. The analogous phenomenon of pairing pseudogap can occur in the attractive model in two dimensions when the pairing fluctuations become critical. Simple analytical expressions for the self-energy are derived in both the magnetic and pairing pseudogap regimes. Other approaches, such as paramagnon, self-consistent fluctuation exchange approximation (FLEX), and pseudo-potential parquet approaches are critically compared. In particular, it is argued that the failure of the FLEX approximation to reproduce the pseudogap and the precursors AFM bands in the weak coupling regime and the Hubbard bands in the strong coupling regime is due to inconsistent treatment of vertex corrections in the expression for the self-energy. Treating the spin fluctuations as if there was a Migdal's theorem can lead not only to quantitatively wrong results but also to qualitatively wrong predictions, in particular with regard to the single-particle pseudogap.

%B Journal De Physique I %V 7 %P 1309–1368 %G eng %0 Journal Article %J Physical Review B %D 1996 %T Crossover from two- to three-dimensional critical behavior for nearly antiferromagnetic itinerant electrons %A Dare, A. M. %A Vilk, Y.M. %A A.-M. S. Tremblay %XThe crossover from two- to three-dimensional critical behavior of nearly antiferromagnetic itinerant electrons is studied in a regime where the interplane single-particle motion of electrons is quantum mechanically incoherent because of thermal fluctuations. This is a relevant regime for very anisotropic materials like the cuprates. The problem is studied within the two-particle self-consistent (TPSC) approach, which has been previously shown to give a quantitative description of Monte Carlo data for the Hubbard model. It is shown that the TPSC approach belongs to the n–>infinity limit of the O(n) universality class. However, contrary to the usual approaches, cutoffs appear naturally in the microscopic TPSC theory so that parameter-free calculations can be done for Hubbard models with. arbitrary band structure. A general discussion of universality in the renormalized-classical crossover from d=2 to d=3 is also given.

%B Physical Review B %V 53 %P 14236–14251 %G eng %0 Journal Article %J Europhysics Letters %D 1996 %T Destruction of Fermi-liquid quasiparticles in two dimensions by critical fluctuations %A Vilk, Y.M. %A A.-M. S. Tremblay %XIt is shown that an analytic approach which includes vertex corrections in a paramagnon-like self-energy can quantitatively explain the two-dimensional Hubbard model in the weak-to-intermediate coupling regime. All parameters are determined self-consistently. This approach clearly shows that in two dimensions Fermi-liquid quasiparticles disappear in the finite-temperature paramagnetic state when the antiferromagnetic correlation length becomes larger than the electronic thermal de Broglie wavelength. Quantum Monte Carlo results are used to compare the accuracy of this approach with others.

%B Europhysics Letters %V 33 %P 159–164 %G eng %0 Conference Proceedings %B XXXIst Rencontres de Moriond %D 1996 %T Luttinger liquids coupled by hopping %A Daniel Boies %A C Bourbonnais %A A.-M. S. Tremblay %E T. Martin %E G. Montambaux %E J. Trân Thanh Vân %B XXXIst Rencontres de Moriond %S Moriond Condensed Matter Physics %C Moriond %V Proceedings of the XXXIst Rencontres de Moriond %P 65-79 %8 1996 %@ 2863322044 %0 Conference Proceedings %B Journal of Physics and Chemistry of Solids %D 1995 %T Destruction of Fermi liquid by spin fluctuations in two dimensions %A Vilk, Y.M. %A A.-M. S. Tremblay %B Journal of Physics and Chemistry of Solids %V 56 %P 1769-1771 %8 12/1995 %0 Journal Article %J Physical Review E %D 1995 %T Field-theory and 2nd Renormalization-group For Multifractals In Percolation %A Fourcade, B. %A A.-M. S. Tremblay %B Physical Review E %V 51 %P 4095–4104 %G eng %0 Journal Article %J Physical Review B %D 1995 %T Magnetic and pair correlations of the Hubbard model with next-nearest-neighbor hopping %A Veilleux, A. F. %A Dare, A. M. %A Chen, L. A. %A Vilk, Y.M. %A A.-M. S. Tremblay %XA combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping t'=-0.35t as a model for high-temperature superconductors. Magnetic properties are analyzed using the two-particle self-consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite t' and at t'=0 but for two totally different physical reasons. When t'=0, it is induced by antiferromagnetic correlations while at t'=-0.35t it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with T-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the d-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed.

%B Physical Review B %V 52 %P 16255–16263 %G eng %0 Journal Article %J International Journal of Modern Physics B %D 1995 %T Nagaoka Ferromagnetism As A Test of Slave-fermion and Slave-boson Approaches %A Boies, D. %A JACKSON, F. A. %A A.-M. S. Tremblay %XThe ferromagnetic to paramagnetic transition in the Nagaoka (U = infinity) limit of the Hubbard Hamiltonian is used to test the applicability of slave-boson and slave-fermion (Schwinger boson) functional-integral approaches. Within the slave-fermion formalism to one-loop order, the ferromagnetic phase is stable to spin-wave, gauge field, and longitudinal fluctuations over a doping interval that is much too large compared with other approaches. Furthermore, nonbipartite lattices such as hcp or fee lattices are ferromagnetic for t > 0 over a wider doping interval than for t < 0, in qualitative disagreement with all other types of calculations. It is possible to remedy all these defects in order to reach agreement, at least qualitatively, with previous studies. It suffices to take the point of view that in the U = infinity limit it is best to represent the paramagnetic phase as the mean-field solution of the slave-boson representation, and the ferromagnetic phase as the mean-field solution of the slave-fermion representation. The transition between both phases is taken to occur at the critical hole doping where the ground state energies are equal. This seems to give the best possible comparison with other approaches, despite the lack of a variational principle justifying comparisons of energies between slave-fermion and slave-boson representations. On bipartite lattices, the critical hole density found analytically by this procedure, delta(c) = 1/3, is identical to the critical density obtained in the Kotliar-Ruckenstein slave-boson approach. This value of delta(c) is also close to various other estimates. Nevertheless, non-bipartite lattices with t > 0 remain ferromagnetic over a small but finite doping interval, in quantitative disagreement with some other approaches.

%B International Journal of Modern Physics B %V 9 %P 1001–1024 %G eng %0 Journal Article %J Physical Review Letters %D 1995 %T One-particle and two-particle instability of coupled luttinger liquids %A Boies, D. %A C Bourbonnais %A A.-M. S. Tremblay %B Physical Review Letters %V 74 %P 968-971 %G eng %0 Journal Article %J Europhysics Letters %D 1995 %T Spiral Magnets As Gapless Mott Insulators %A René Côté %A A.-M. S. Tremblay %XIn the large-U limit, the ground state of the half-filled, nearest-neighbor Hubbard model on the triangular lattice is the three-sublattice antiferromagnet. In sharp contrast with the square-lattice case, where Goldstone modes never have a charge component, it is shown that beyond leading order in t/U the three Goldstone modes on the triangular lattice, at finite q, are a linear combination of spin and charge. This leads to non-vanishing conductivity at any finite frequency, even though the magnet remains insulating at zero frequency. More generally, non-collinear spin order should lead to such gapless insulating behavior.

%B Europhysics Letters %V 29 %P 37–42 %8 01/1995 %G eng %U http://stacks.iop.org/0295-5075/29/37 %0 Journal Article %J Physica C %D 1994 %T 2-particle Self-consistent Theory For Spin and Charge Fluctuations In the Hubbard-model %A Vilk, Y.M. %A Chen, L. %A A.-M. S. Tremblay %XA theory which is self-consistent at the two-particle level is presented for both spin and charge fluctuations in the Hubbard model. It is in quantitative agreement with Monte Carlo data at least up to intermediate coupling (U similar to 8t) It includes both short-wavelength quantum renormalization effects, and long-wavelength thermal fluctuations which can destroy long-range order in two dimensions. This last effect leads to a small energy scale, as often observed in high temperature superconductors. The theory is conserving, satisfies the Pauli principle and includes three-particle correlations necessary to account for the incipient Mott transition.

%B Physica C %V 235 %P 2235–2236 %G eng %U http://www.sciencedirect.com/science/article/pii/0921453494923396 %0 Journal Article %J Physical Review B %D 1994 %T Comparisons Between Monte-carlo Simulations and A Simple Crossing-symmetrical Approach To the Hubbard-model At Low-density %A Daré, A. M. %A Chen, L. %A A.-M. S. Tremblay %XA simple crossing-symmetric approximation for the fully reducible vertex is compared with Monte Carlo simulations of the two-dimensional Hubbard model. Up to quarter-filling, in the intermediate coupling regime, accuracies better than 10% are obtained for several static correlation functions, including spin and charge, as well as the pairing channels most widely studied in the context of high-T(c) superconductivity. The accuracy is generally better for the pairing channels. The results shed light on the applicability of the renormalized generalized-random-phase-approximation scheme, its relation to Fermi-liquid theory, and on the regime where nontrivial effects may appear in pairing channels. The approximation under study consists in assuming that for parallel spins the fully reducible particle-particle vertex vanishes, while for antiparallel spins it is equal to the T matrix. The fully reducible particle-hole vertex is then obtained from the latter vertex by using crossing symmetry. This simple approximation is not conserving but it preserves global symmetries. It suggests that Monte Carlo results for the two-dimensional Hubbard model in small systems at low density and intermediate coupling can be interpreted using a weakly correlated Fermi-liquid picture.

%B Physical Review B %V 49 %P 4106–4118 %G eng %0 Journal Article %J Physica B %D 1994 %T Correlation-functions of the Hubbard-model At Low-density In A Crossing-symmetrical Approximation - Comparisons With Monte-carlo Simulations %A Daré, A. M. %A Chen, L. %A A.-M. S. Tremblay %XThe accuracy of a simple crossing-symmetric approximation for the fully reducible vertex is tested by comparisons of the spin, charge, and pairing correlations with those obtained by Monte Carlo simulations of the two-dimensional Hubbard model. The approximation under study consists in assuming that for parallel spins the fully reducible vertex vanishes, while for anti-parallel spins it is equal to the T-matrix. Up to quarter-filling, accuracies better than 10% are obtained.

%B Physica B %V 194 %P 1413–1414 %G eng %0 Journal Article %J Physical Review B %D 1994 %T Magnetic-susceptibility of the two-dimensional Hubbard-model - Comment %A Chen, L. A. %A A.-M. S. Tremblay %XThe observed magnetic spin susceptibility of high-temperature superconductors such as La2-xSrxCuO4 increases when x increases from zero, i.e., as one dopes away from half-filling. Recent Monte Carlo simulations of A. Moreo [Phys. Rev. B 48, 3380 (1993)] suggest that this behavior can be reproduced by the two-dimensional Hubbard model only at large coupling, namely, U/t of order 10. Using longer runs, our Monte Carlo simulations show that the same behavior as for U/t = 10 is obtained even in the intermediate coupling regime (U/t = 4), as long as the temperature is low enough (T = t/6) that strong antiferromagnetic correlations are building up at half-filling. These results are consistent with the fact that in two dimensions, the generalized random phase approximation should fail in the pa-rameter range where it predicts a magnetic phase transition.

%B Physical Review B %V 49 %P 4338–4340 %G eng %0 Conference Proceedings %B Superconducting Symposium 1994 %D 1994 %T Quantum Monte Carlo simulations for a model of high-tem¬perature superconductors: effect of next-nearest-neighbor hopping %A Veilleux, A. F. %A Daré, A.-M. %A Chen, L. %A Vilk, Y.M. %A A.-M. S. Tremblay %E John W. Ross %B Superconducting Symposium 1994 %V University of Toronto Press %P 78-85 %8 1994 %0 Journal Article %J Physical Review B %D 1994 %T Theory of Spin and Charge Fluctuations In the Hubbard-model %A Vilk, Y.M. %A Chen, L. %A A.-M. S. Tremblay %XA self-consistent theory of both spin and charge fluctuations in the Hubbard model is presented. It is in quantitative agreement with Monte Carlo data at least up to intermediate coupling (U approximately 8t). It includes both short-wavelength quantum renormalization effects, and long-wavelength thermal fluctuations, which can destroy long-range order in two dimensions. This last effect leads to a small energy scale, as often observed in high-temperature superconductors. The theory is conserving, satisfies the Pauli principle, and includes three-particle correlations necessary to account for the incipient Mott transition.

%B Physical Review B %V 49 %P 13267–13270 %G eng %0 Journal Article %J Physical Review B %D 1993 %T Flux-quantization In Rings For Hubbard (attractive and Repulsive) and T-j-like Hamiltonians - Comment %A Chen, L. %A Mei, C. J. %A A.-M. S. Tremblay %XIt is shown for three models with strong correlations that the value of the total spin of the ground state of finite-size rings with two fermions (holes or electrons) can change as a function of magnetic flux PHI. It is concluded that the magnetic flux periodicity may be used as a test of binding only if one also checks for changes in spin quantum numbers.

%B Physical Review B %V 47 %P 15316–15318 %G eng %0 Journal Article %J Physical Review B %D 1993 %T Magnetic Neutron-scattering From 2-dimensional Lattice Electrons - the Case of La2-xsrxcuo4 %A Bénard, P. %A Chen, L. %A A.-M. S. Tremblay %XIt is found that the one-band Hubbard model, in the weak- to intermediate-coupling regime, can account qualitatively for magnetic-neutron-scattering experiments in the paramagnetic phase of La2-xSrxCuO4 when second-neighbor hopping is included. However, the peak positions, which in two dimensions are determined mostly by the band structure, cannot agree quantitatively with the experimental results when concentration-independent band parameters are used. More importantly, while the energy scale of roughly 150 K seen in the experiments can come from second-neighbor hopping, it arises most naturally if one is very close to a magnetic instability. The proximity to a magnetic instability can be checked experimentally by measuring the relative size of the lattice equivalent of 2k(F) anomalies that appear closer to the origin in wave-vector space. Such lattice-2k(F) anomalies would allow magnetic neutron scattering to become a spectroscopic tool for the two-dimensional Fermi surface. Finally, exact results are also given for the imaginary part of the Lindhard function on the square lattice.

%B Physical Review B %V 47 %P 15217–15241 %G eng %0 Journal Article %J Physical Review B %D 1993 %T Neutron-scattering Measurements As A Test of Theories of High-temperature Superconductivity %A Bénard, P. %A Chen, L. %A A.-M. S. Tremblay %XIt is shown that the Hubbard model in the intermediate-coupling regime can qualitatively explain neutron-scattering experiments in La2-xSrxCuO4 only if there are strong magnetic fluctuations in the system. By contrast, the marginal-Fermi-liquid approach explains the data without appealing at all to strong magnetic fluctuations. It is shown that the strength of the magnetic fluctuations can be estimated by detecting incommensurate peaks located near the zone center using neutron-scattering experiments.

%B Physical Review B %V 47 %P 589–592 %G eng %0 Journal Article %J Journal De Physique I %D 1993 %T Scaling Behavior of Multifractal-moment Distributions Near Criticality %A Albinet, G. %A A.-M. S. Tremblay %A A.-M. S. Tremblay %XSample to sample fluctuations of the multifractal moments of percolating random-resistor networks are studied via Monte Carlo simulations. For systems of size L, these fluctuations depend on DELTAp, the deviation from the critical concentration, only through the scaled variable DELTApL1/nu. At DELTAp = 0, these fluctuations depend on h, the ratio of the good and bad conductances, only through hL(phi). This is consistent with a previously proposed scaling ansatz for the joint probability distribution of multifractal moments. In the DELTAp not-equal 0 direction, the relative fluctuations are largest when the bulk correlation length is of the order of L.

%B Journal De Physique I %V 3 %P 323–330 %G eng %0 Journal Article %J Journal of Physics and Chemistry of Solids %D 1993 %T Symmetry and Nodes of the Superconducting Gap %A Chen, L. A. %A A.-M. S. Tremblay %XFor pairing potentials which act only in the vicinity of the Fermi-surface, a Fermi-surface harmonics expansion of the gap function is appropriate. After a general symmetry discussion, it is pointed-out that the first extended s-wave occuring in the Fermi-surface harmonics expansion of the gap function a) is closely related to the usual d-waves b) it can have a large number of nodes. This may reconcile the experiments which see nodes in the gap and neutron-scattering experiments which cannot resolve the anistropy in the gap function.

%B Journal of Physics and Chemistry of Solids %V 54 %P 1381–1384 %G eng %0 Journal Article %J International Journal of Modern Physics B %D 1992 %T Determinant Monte-carlo For the Hubbard-model With Arbitrarily Gauged Auxiliary Fields %A Chen, L. %A A.-M. S. Tremblay %XMonte Carlo methods for the Hubbard model rely on a Hubbard-Stratonovich (HS) decomposition (auxiliary field method) to perform importance sampling on classical variables. Freedom in the choice of the local HS fields can be formally seen as a gauge choice. While the choice of gauge does not influence observable quantities, it may influence intermediate quantities in the calculation, such as the famous "fermion sign", and it may also influence the efficiency with which the algorithm explores phase space. The effect of arbitrary gauge choices on both aspects of the algorithm are investigated. It is found that in the single spin-flip determinantal approach, certain gauges lead to a better exploration of phase space. This improvement is demonstrated, in the intermediate coupling regime, by histograms which for the first time show the behavior expected from grand canonical simulations. It is also found that the improved phase space exploration can in practice offset the apparent disadvantage of a smaller fermion sign.

%B International Journal of Modern Physics B %V 6 %P 547–560 %G eng %U https://www.worldscientific.com/doi/abs/10.1142/S0217979292000323 %0 Journal Article %J Physica A %D 1992 %T How Many Correlation Lengths For Multifractals %A A.-M. S. Tremblay %A A.-M. S. Tremblay %A Albinet, G. %A Fourcade, B. %XIt is shown, here in the context of percolation, that one can have multifractal behavior and at the same time a single correlation length. This length sets the scale below which non-trivial scaling behavior occurs and it is controlled by a few relevant operators. as in ordinary critical phenomena. All other correlation lengths may be obtained from simple metric factors. The quantities which lead to an infinite set of exponents are described by a second renormalization group which is slaked to the first one which determines the correlation length. The results are relevant also to the problem of noise in percolating systems.

%B Physica A %V 183 %P 398–410 %G eng %0 Journal Article %J Physical Review B %D 1992 %T Noise and Crossover Exponent In Conductor-insulator Mixtures and Superconductor-conductor Mixtures %A A.-M. S. Tremblay %A Albinet, G. %A A.-M. S. Tremblay %XThe resistance noise of random conductor-insulator mixtures is studied in the case where the insulators have a small but finite conductance. The conductance noise of superconductor-conductor mixtures is similarly studied when the superconductors have a small but finite resistance. The Migdal-Kadanoff renormalization-group calculations that lead to the appropriate linear and nonlinear scaling fields for these problems are discussed in detail. The corresponding homogeneity relations for the total noise are valid near the unstable percolation fixed point whatever the relative size of the microscopic noises. The exponents of the superconductor-conductor mixture appear naturally in the scaling form of the noise coming from the imperfect insulators. Analogously, the exponents of the conductor-insulator mixture enter in the scaling form of the noise coming from the imperfect superconductors in the superconductor-conductor problem. Monte Carlo simulations in two and three dimensions confirm that the scaling predictions are valid well beyond the domain of applicability of the Migdal-Kadanoff approach. For all multifractal moments and both types of mixtures, there is a single crossover exponent and a single correlation length associated with the ratio of the microscopic conductances.

%B Physical Review B %V 45 %P 755–767 %G eng %0 Journal Article %J Physical Review B %D 1992 %T One-dimensional vibrations and disorder - the Zr1-xhfxs3 solid-solution %A Ait-Ouali, A. %A S. Jandl %A Marinier, P. %A Lopez-Castillo, J.M. %A A.-M. S. Tremblay %XIn the trichalcogenide family of compounds Zr1-xHfxS3 there is a frequency range where the optic modes are expected to be describable by a simple one-dimensional model. It is shown that the disorder-induced linewidth in the relevant frequency range could be consistent with theoretical calculations for a simple diatomic chain model. The vibrations involved are along the chain direction and are of B(g) type. All the B(g) modes of this family of compounds are also here unequivocally identified.

%B Physical Review B %V 46 %P 5183–5193 %G eng %0 Conference Paper %B 10th Specialized Colloque AMPERE, NMR/NQR in High-Tc Superconductors %D 1991 %T The influence of spin fluctuations on the temperature dependance of the magnetic susceptibility and nuclear relaxation in high Tc superconductors %A T.W. Li %A C Bourbonnais %A Chen, L. %A A.-M. S. Tremblay %E D. Brinkmann %B 10th Specialized Colloque AMPERE, NMR/NQR in High-Tc Superconductors %C Zurich, Suisse %8 08/1991 %0 Journal Article %J Physical Review Letters %D 1991 %T Magnetic-properties of the 2-dimensional Hubbard-model %A Chen, L. %A C Bourbonnais %A Li, T. %A A.-M. S. Tremblay %XMonte Carlo simulations of the magnetic structure factor of the two-dimensional Hubbard model are in qualitative agreement with the slave-boson approach and, in the low-temperature intermediate-coupling limit, they are in even better quantitative agreement with the random-phase approximation, as long as a renormalized repulsion U is used. This renormalization comes from maximally crossed diagrams, which account for two-body short-range correlations. One of the consequences is that Stoner ferromagnetism is not a generic property of the two-dimensional one-band Hubbard model.

%B Physical Review Letters %V 66 %P 369–372 %G eng %0 Journal Article %J Physical Review B %D 1991 %T Noise and crossover exponent In the two-component random resistor network %A A.-M. S. Tremblay %A Albinet, G. %A A.-M. S. Tremblay %XThe resistance noise of random conductor-insulator mixtures is studied in the case where the insulator has a small, but finite conductivity. Based on the structure of a simple renormalization group, a general homogeneity relation for the noise of both insulators and conductors is suggested. The expression for the total noise is valid from the noisy-conductor quiet-insulator limit to the quiet-conductor noisy-insulator limit. Monte Carlo simulations confirm the scaling predictions. For all multifractal moments, there is a single crossover exponent associated with the small finite conductivity of the insulator.

%B Physical Review B %V 43 %P 11546–11549 %G eng %0 Journal Article %J Journal of Applied Physics %D 1991 %T Random Mixtures With Orientational Order, and the Anisotropic Resistivity Tensor of High-t(c) Superconductors %A Diazguilera, A. %A A.-M. S. Tremblay %XBy generalizing effective-medium theory to the case of orientationally ordered but positionally disordered two-component mixtures, it is shown that the anisotropic dielectric tensor of oxide superconductors can be extracted from microwave measurements on oriented crystallites of YBa2Cu3O7-x embedded in epoxy. Surprisingly, this technique appears to be the only one which can access the resistivity perpendicular to the copper-oxide planes in crystallites that are too small for depositing electrodes. This possibility arises in part because the real part of the dielectric constant of oxide superconductors has a large magnitude . The validity of the effective-medium approach for orientationally ordered mixtures is corroborated by simulations on two-dimensional anisotropic random resistor networks. Analysis of the experimental data suggests that the zero-temperature limit of the finite-frequency resistivity does not vanish along the c axis, a result which would imply the existence of states at the Fermi surface even in the superconducting state.

%B Journal of Applied Physics %V 69 %P 379–383 %G eng %0 Journal Article %J Physical Review Letters %D 1990 %T Amplitudes of Multifractal Moments At the Onset of Chaos - Universal Ratios and Crossover Functions %A Fourcade, B. %A A.-M. S. Tremblay %B Physical Review Letters %V 64 %P 2659–2662 %G eng %0 Journal Article %J Physical Review Letters %D 1990 %T Breakdown of Multifractal Behavior In Diffusion-limited Aggregates - Comment %A Fourcade, B. %A A.-M. S. Tremblay %B Physical Review Letters %V 64 %P 1842–1842 %G eng %0 Conference Proceedings %B Supercomputing Symposium '90 %D 1990 %T Monte Carlo Method for Strongly Interacting Electrons %A A.-M. S. Tremblay %A C. Boily %A Chen, L. %A Nelisse, H. %A Reid, A. %E Dominique Pelletier %B Supercomputing Symposium '90 %C Montréal %V Proceedings of Supercomputing Symposium '90 %P 197-210 %8 1990 %0 Journal Article %J Journal of Statistical Physics %D 1990 %T Universal Multifractal Properties of Circle Maps From the Point-of-view of Critical Phenomena .2. Analytical Results %A Fourcade, B. %A A.-M. S. Tremblay %XThe multifractal properties of maps of the circle exhibited in the preceding paper are analyzed from a simplified approach to the renormalization group of Kadanoff. This "second" renormalization group transformation, whose formulation and interpretation are discussed here, acts on the space of one-time-differentiable coordinate changes which associate a map on the critical manifold to the fixed point of the usual renormalization group. While the dependence of the multifractal moments on the starting point can be described statistically, and in particular through universal amplitude ratios as in paper I, it is shown that Fourier analysis is another possible approach. For all multifractal moments, the low-frequency Fourier coefficients have a universal self-similar scaling behavior analogous to that found for the usual spectrum of circle maps. In the case the first moment, it is demonstrated that the Fourier coefficients are, within constants, equal to the usual spectrum. The relation between amplitude ratios and Fourier coefficients is established and it is demonstrated that the universal values of the ratios come from the universal low-frequency Fourier coefficients. Since, for the universal ratios arising in the statistical description, the scaling regime is much more easily accessible than for the spectrum, the statistical approach described in paper I should be more convenient for experiments and could become an alternative to the usual spectral description. The universal statistical description of the multifractal moments adopted here is possible because the choice of the a priori probability for the starting point is demonstrated to be irrelevant.

%B Journal of Statistical Physics %V 61 %P 639–665 %G eng %0 Journal Article %J Journal of Statistical Physics %D 1990 %T Universal Multifractal Properties of Circle Maps From the Point-of-view of Critical Phenomena .1. Phenomenology %A Fourcade, B. %A A.-M. S. Tremblay %XThe strange attractor for maps of the circle at criticality has been shown to be characterized by a remarkable infinite set of exponents. This characterization by an infinite set of exponents has become known as the "multifractal" approach. The present paper reformulates the multifractal properties of the strange attractor in a way more akin to critical phenomena. This new approach allows one to study the universal properties of both the critical point and of its vicinity within the same framework, and it allows universal properties to be extracted from experimental data in a straightforward manner. Obtaining Feigenbaum's scalling function from the experimental data is, by contrast, much more difficult. In addition to the infinite set of exponents, universal amplitude ratios here appear naturally. To study the crossover region near criticality, a "correlation time," which plays a role analogous to the "correlation length" in critical phenomena, is introduced. This new approach is based on the introduction of a joint probability distribution for the positive integer moments of the closest-return distances. This joint probability distribution is physically motivated by the large fluctuations of the multifractal moments with respect to the choice of origin. The joint probability distribution has scaling properties analogous to those of the free energy close to a critical point.

%B Journal of Statistical Physics %V 61 %P 607–637 %G eng %0 Journal Article %J Physical Review B %D 1989 %T Fermi surface of the one-dimensional Hubbard model %A C Bourbonnais %A Nélisse, H. %A Reid, A. %A A.-M. S. Tremblay %B Physical Review B %V 40 %P 2297-2303 %G eng %0 Conference Proceedings %B M2S-HTSC %D 1989 %T Fermi surface of the one-dimensional Hubbard model: Finite-size effects %A C Bourbonnais %A Nelisse, H. %A Reid, A. %A A.-M. S. Tremblay %E R.N. Shelton %E W.A. Harrison %E N.E. Philips %B M2S-HTSC %V Physica C: 162-164 %P 805-806 %8 1989 %0 Journal Article %J Physica C: Superconductivity and its applications %D 1989 %T Fermi surface of the one-dimensional Hubbard model: Finite-size effects %A C Bourbonnais %A Nelisse, H. %A Reid, A. %A A.-M. S. Tremblay %B Physica C: Superconductivity and its applications %V 162-164 %P 805-806 %G eng %0 Journal Article %J Physical Review B %D 1989 %T Finite-size Effects In Continuum Percolation %A A.-M. S. Tremblay %A MACHTA, J. %B Physical Review B %V 40 %P 5131–5139 %G eng %0 Journal Article %J Physical Review B %D 1989 %T Infinite Set of Crossover Exponents of the Xy Model and F(a) Approach %A Fourcade, B. %A A.-M. S. Tremblay %B Physical Review B %V 39 %P 6819–6822 %G eng %0 Conference Proceedings %B Physica A %D 1989 %T Multifractals and Noise in Metal-Insulator Mixtures %A A.-M. S. Tremblay %A Fourcade, B. %A Breton, P. %B Physica A %V 157 %P 89-100 %8 1989 %0 Journal Article %J Physical Review B %D 1989 %T Negative Moments of Currents In Percolating Resistor Networks %A Aharony, A. %A Blumenfeld, R. %A Breton, P. %A Fourcade, B. %A Harris, A. B. %A Meir, Y. %A A.-M. S. Tremblay %B Physical Review B %V 40 %P 7318–7320 %G eng %0 Conference Proceedings %B Universalities in Condensed Matter %D 1988 %T Multifractal analysis in the circle map: Analogies with critical phenomena %A Fourcade, B. %A A.-M. S. Tremblay %E R. Jullien %E L. Peliti %E Rammal, R. %E N. Boccara %B Universalities in Condensed Matter %S Springer Proceedings in Physics %7 Springer-Verlag Berlin %V Springer Proceedings in Physics : 32 %P 183-187 %8 1988 %0 Conference Proceedings %B XVIIth International Colloquium on Group Theoretical Methods in Physics %D 1988 %T Observable infinite sets of exponents in multifractals and in critical phenomena: the role of symmetry %A A.-M. S. Tremblay %A Fourcade, B. %E Y. Saint-Aubin %E L. Vinet %B XVIIth International Colloquium on Group Theoretical Methods in Physics %C Saint-Adèle, Canada %V World Scientific, Singapore %P 137-153 %8 1989 %0 Magazine Article %D 1988 %T Renormalization group, fractals & multifractals %A A.-M. S. Tremblay %B Canadian Research %V 21 %P 11-14/29-30 %8 03/1988 %N 3 %9 Application notes %6 8 times a year %0 Journal Article %J Physical Review B %D 1988 %T Reply to Comment on the conductivity exponent in continuum percolation %A Lubensky, T.C. %A A.-M. S. Tremblay %B Physical Review B %V 37 %P 7894-7895 %G eng %0 Conference Proceedings %B Universalities in Condensed Matter %D 1988 %T Universal properties of multifractal moments: Analogies with critical phenomena %A A.-M. S. Tremblay %A Fourcade, B. %E R. Jullien %E L. Peliti %E Rammal, R. %E N. Boccara %B Universalities in Condensed Matter %S Springer Proceedings in Physics %7 Springer-Verlag Berlin %C Heidelberg %V Springer Proceedings in Physics : 32 %P 176-182 %8 1988 %0 Journal Article %J Physical Review A %D 1987 %T Anomalies in the multifractal analysis of self-similar resistor networks %A Fourcade, B. %A A.-M. S. Tremblay %B Physical Review A %V 36 %P 2352-2358 %G eng %0 Journal Article %J Comptes-rendus de l'Académie des Sciences à Paris %D 1987 %T Antiferromagnétisme et champs cristallins dans les oxydes de cuivre supraconducteurs %A Ambegaokar, V. %A P.G. DeGennes %A A.-M. S. Tremblay %B Comptes-rendus de l'Académie des Sciences à Paris %V 305 %P 757-760 %8 1987 %N Série II %0 Journal Article %J Physical Review B %D 1987 %T Densities of states, projected densities of states, and transfer-matrix methods from a unified point of view %A Lemieux, M.-A. %A A.-M. S. Tremblay %B Physical Review B %V 36 %P 1463-1474 %G eng %0 Conference Proceedings %B 1987 IEEE International Symposium on Circuits and Systems %D 1987 %T Electrical properties of fractal networks (and why). %A A.-M. S. Tremblay %B 1987 IEEE International Symposium on Circuits and Systems %C Philadelphie, Pennsylvanie %V Proceedings of the 1987 IEEE International Symposium on Circuits and Systems %P 956-959 %8 1987 %0 Conference Proceedings %B Annales des sciences mathématiques du Québec %D 1987 %T Famille d'exposants pour les propriétés électriques des fractals %A A.-M. S. Tremblay %A Fourcade, B. %A Breton, P. %B Annales des sciences mathématiques du Québec %V 11 %P 183-204 %8 1987 %0 Journal Article %J Physical Review B %D 1987 %T Multifractals and critical phenomena in percolating networks: Fixed point, gap scaling, and universality %A Fourcade, B. %A Breton, P. %A A.-M. S. Tremblay %B Physical Review B %V 36 %P 8925-8928 %G eng %0 Conference Proceedings %B 9th International Conference on Noise in Physical Systems %D 1987 %T Noise in metal-insulator composites %A A.-M. S. Tremblay %A Fourcade, B. %E C.M. Van Vliet %B 9th International Conference on Noise in Physical Systems %7 World Scientific Singapore %C Montréal %V Proceedings of the 9th International Conference on Noise in Physical Systems %P 59-69 %8 1987 %0 Journal Article %J Physical Review Letters %D 1987 %T Resistance noise in nonlinear resistor networks %A Rammal, R. %A A.-M. S. Tremblay %B Physical Review Letters %V 58 %P 415-418 %G eng %0 Journal Article %J Journal of Physics A: Mathematical and General %D 1986 %T Anomalous diffusion on fractal lattices with site disorder %A Robillard, S. %A A.-M. S. Tremblay %B Journal of Physics A: Mathematical and General %V 19 %P 2171-2181 %G eng %0 Journal Article %J Physica A: Statistical Mechanics and its Applications %D 1986 %T Comment on the role of thermodynamic representations in the study of fluids in far from equilibrium steady states %A Llebot, J.E. %A A.-M. S. Tremblay %B Physica A: Statistical Mechanics and its Applications %V 135 %P 289-293 %G eng %0 Journal Article %J Physical Review B %D 1986 %T Diffusion noise of fractal networks and percolation clusters %A Fourcade, B. %A A.-M. S. Tremblay %B Physical Review B %V 34 %P 7802-7812 %G eng %0 Journal Article %J Physics Letters A %D 1986 %T Dynamical phase transitions in hierarchical structures %A A.-M. S. Tremblay %B Physics Letters A %V 116 %P 329-330 %G eng %0 Journal Article %J Physical Review Letters %D 1986 %T Erratum: Splay rigidity in the diluted central-force elastic network (Physical Review Letters (1986) 57, 2 (274)) %A A.-M. S. Tremblay %A Day, A.R. %A A.-M. S. Tremblay %B Physical Review Letters %V 57 %P 274 %G eng %0 Journal Article %J Physical Review B %D 1986 %T Expansion for transport exponents of continuum percolating systems %A Lubensky, T.C. %A A.-M. S. Tremblay %B Physical Review B %V 34 %P 3408-3417 %G eng %0 Journal Article %J Physical Review B %D 1986 %T Exponents for 1/f noise, near a continuum percolation threshold %A A.-M. S. Tremblay %A Feng, S. %A Breton, P. %B Physical Review B %V 33 %P 2077-2080 %G eng %0 Journal Article %J Physical Review B %D 1986 %T Light scattering spectrum of one-dimensional mixed crystals %A Lopez Castillo, J.M.L. %A A.-M. S. Tremblay %B Physical Review B %V 33 %P 6599-6611 %G eng %0 Journal Article %J Physical Review B %D 1986 %T Linewidths from sum rules in mixed crystals %A Lopezcastillo, J. M. %A A.-M. S. Tremblay %B Physical Review B %V 34 %P 8482-8485 %G eng %0 Journal Article %J Physical Review Letters %D 1986 %T Rigid Backbone: A New Geometry for Percolation %A Day, A.R. %A A.-M. S. Tremblay %A A.-M. S. Tremblay %B Physical Review Letters %V 56 %P 2501-2504 %G eng %0 Journal Article %J Physical Review Letters %D 1986 %T Splay rigidity in the diluted central-force elastic network %A A.-M. S. Tremblay %A Day, A.R. %A A.-M. S. Tremblay %B Physical Review Letters %V 56 %P 1425 %G eng %0 Journal Article %J Physical Review A %D 1985 %T 1/f noise in random resistor networks: Fractals and percolating systems %A Rammal, R. %A Tannous, C. %A A.-M. S. Tremblay %B Physical Review A %V 31 %P 2662-2671 %G eng %0 Journal Article %J Physical Review Letters %D 1985 %T Comment on ``$ε$ expansion for the conductivity of a random resistor network'' %A Rammal, R. %A Lemieux, M.-A. %A A.-M. S. Tremblay %B Physical Review Letters %V 54 %P 1087 %G eng %0 Journal Article %J Physical Review Letters %D 1985 %T Flicker (1f) noise in percolation networks: A new hierarchy of exponents %A Rammal, R. %A Tannous, C. %A Breton, P. %A A.-M. S. Tremblay %B Physical Review Letters %V 54 %P 1718-1721 %G eng %0 Journal Article %J Physics Letters A %D 1985 %T Long-range correlations for diffusion in a random medium %A Rubi, M. %A A.-M. S. Tremblay %B Physics Letters A %V 111 %P 33-35 %G eng %0 Journal Article %J Journal of Non-Crystalline Solids %D 1985 %T Spectral properties of percolating central force elastic networks %A Day, A.R. %A Tremblay, R. %A A.-M. S. Tremblay %B Journal of Non-Crystalline Solids %V 75 %P 245-251 %G eng %0 Journal Article %J Journal de physique - Lettres %D 1985 %T Unified Approach to Numerical Transfer Matrix Methods for Disordered Systems: Applications to Mixed Crystals and to Elasticity Percolation %A Lemieux, M.A. %A Breton, P. %A A.-M. S. Tremblay %B Journal de physique - Lettres %V 46 %P L1-L7 %8 1985 %& L-1 %0 Journal Article %J Journal de physique - Lettres %D 1984 %T A.C. Response of Fractal Networks %A J.P. Clerc %A A.-M. S. Tremblay %A Albinet, G. %A C.D. Mitescu %B Journal de physique - Lettres %V 45 %P L-913/11-12 %8 1984 %& L-913 %0 Journal Article %J Physics Letters A %D 1984 %T On the linear specific heat of disordered solids at low temperatures %A Dandoloff, R. %A A.-M. S. Tremblay %B Physics Letters A %V 102 %P 245-246 %G eng %0 Journal Article %J Physical Review A %D 1984 %T Liquid-expanded liquid-condensed phase transition in amphiphilic monolayers: A renormalization-group approach to chiral-symmetry breaking of hydrocarbon-chain defects %A Legré, J.-P. %A Albinet, G. %A Firpo, J.-L. %A A.-M. S. Tremblay %B Physical Review A %V 30 %P 2720-2729 %G eng %0 Conference Proceedings %B Phonon Scattering in Condensed Matter %D 1984 %T Nonequilibrium Phonon Distribution in a Quantizing Magnetic Field: A Tunable GHz to THz Phonon Generator? %A Slater, G.W. %A A.-M. S. Tremblay %E W. Eisenmenger %E K. LaBmann %E S. Döttinger %B Phonon Scattering in Condensed Matter %S Springer-Verlag, Berlin %V Springer-Verlag Berlin %P 49/51 %8 1984 %0 Journal Article %J Journal of Applied Physics %D 1984 %T Position-space rescaling and hierarchical lattice models of disordered one-dimensional systems (invited) %A A.-M. S. Tremblay %A Breton, P. %B Journal of Applied Physics %V 55 %P 2389-2394 %G eng %0 Conference Proceedings %B Recent Developments in Nonequilibrium Thermodynamics %D 1984 %T Theories of Nonequilibrium Fluctuations %A A.-M. S. Tremblay %E J.S. Casas-Vàsquez %E D. Jou %E G. Lebon %B Recent Developments in Nonequilibrium Thermodynamics %V Springer-Verlag Berlin %P 267-315 %8 1984 %0 Journal Article %J Physical Review B %D 1984 %T Tunable quantum hypersound generator in the gigahertz to terahertz range %A Slater, G.W. %A A.-M. S. Tremblay %B Physical Review B %V 29 %P 2289-2292 %G eng %0 Journal Article %J Physical Review A %D 1983 %T Chain fusion and orientational ordering in monomolecular layers of amphiphilic molecules %A Albinet, G. %A A.-M. S. Tremblay %B Physical Review A %V 27 %P 2206-2216 %G eng %0 Journal Article %J Physical Review B %D 1983 %T Chaotic scaling trajectories and hierarchical lattice models of disordered binary harmonic chains %A Langlois, J.-M. %A A.-M. S. Tremblay %A Southern, B.W. %B Physical Review B %V 28 %P 218-231 %G eng %0 Journal Article %J Physical Review B %D 1983 %T Disordered binary harmonic chains with site-dependent force constants %A Albinet, G. %A A.-M. S. Tremblay %B Physical Review B %V 28 %P 232-235 %G eng %0 Conference Proceedings %B Noise in Physical Systems and 1/f Noise %D 1983 %T Fluctuations in Dissipative Steady States of Thin Metallic Films %A A.-M. S. Tremblay %A François Vidal %E M. Savelli %E G. Lecoy %E J.-P. Nougier %B Noise in Physical Systems and 1/f Noise %S Elsevier Science Publishers B.V. %V Elsevier Science Publishers B.V. %P 53-55 %8 1983 %0 Journal Article %J Physical Review B %D 1983 %T Real-space rescaling method for the spectral properties of tight-binding systems %A Southern, B.W. %A Kumar, A.A. %A Loly, P.D. %A A.-M. S. Tremblay %B Physical Review B %V 27 %P 1405-1408 %G eng %0 Journal Article %J Journal de physique - Lettres %D 1983 %T Scalling and Density of States of Fractal Lattices form a Generating Function Point of View %A A.-M. S. Tremblay %A Southern, B.W. %B Journal de physique - Lettres %V 44 %P L-843/1-10 %8 1983 %& L-843 %0 Conference Proceedings %B Les Embiez - 27-29 sept 1982 %D 1982 %T Application du groupe de renormalisation à l'étude des monocouches de molécules amphiphiles %A Albinet, G. %A A.-M. S. Tremblay %B Les Embiez - 27-29 sept 1982 %C Ile des Embiez, France %V Physique des surfaces et interfaces %P 16-23 %8 1983 %0 Journal Article %J Physical Review B %D 1982 %T Fluctuations in dissipative steady states of thin metallic films %A A.-M. S. Tremblay %A Vidal, F. %B Physical Review B %V 25 %P 7562-7576 %G eng %0 Journal Article %J Physical Review A %D 1982 %T Thermal fluctuations in the presence of two dissipative steady-state currents %A Tremblay, C. %A A.-M. S. Tremblay %B Physical Review A %V 25 %P 1692-1698 %G eng %0 Journal Article %J Journal of Statistical Physics %D 1981 %T Deviation of 1/f voltage fluctuations from scale-similar Gaussian behavior %A Nelkin, M. %A A.-M. S. Tremblay %B Journal of Statistical Physics %V 25 %P 253-268 %G eng %0 Journal Article %J Physical Review B %D 1981 %T Equilibrium resistance fluctuations %A A.-M. S. Tremblay %A Nelkin, M. %B Physical Review B %V 24 %P 2551-2566 %G eng %0 Journal Article %J Physical Review A %D 1981 %T Erratum: Fluctuations about simple nonequilibrium steady states (Physical Review A (1981) 24, 3, (1655-1656)) %A A.-M. S. Tremblay %A Arai, M. %A Siggia, E.D. %B Physical Review A %V 24 %P 1655-1656 %G eng %0 Journal Article %J Physical Review A %D 1981 %T Fluctuations about simple nonequilibrium steady states %A A.-M. S. Tremblay %A Arai, M. %A Siggia, E.D. %B Physical Review A %V 23 %P 1451-1480 %G eng %0 Journal Article %J Physics Letters A %D 1980 %T Fluctuations about hydrodynamic nonequilibrium steady states %A A.-M. S. Tremblay %A Siggia, E.D. %A Arai, M. %B Physics Letters A %V 76 %P 57-60 %G eng %0 Journal Article %J Annals of Physics %D 1980 %T Kinetic Equations in Superconductors and the Nature and Decay Rate of the New Mode %A A.-M. S. Tremblay %A Bruce R. Patton %A P.C. Martin %B Annals of Physics %V 124 %P 401/1-48 %8 1980 %0 Conference Proceedings %B NATO Advanced Study Institute on Nonequilibrium Superconductivity, Phonons and Kapitza Boundaries %D 1980 %T Stability of nonequilibrium superconducting states I : General principles %A A.-M. S. Tremblay %E K.E. Gray %B NATO Advanced Study Institute on Nonequilibrium Superconductivity, Phonons and Kapitza Boundaries %C Acqua Fredda di Maratea, Italy %V Proceedings of the NATO Advanced Study Institute on Nonequilibrium Superconductivity, Phonons and Kapitza Boundaries Chapter 10 %P 289-307 %8 1981 %0 Conference Proceedings %B NATO Advanced Study Institute on Nonequilibrium Superconductivity, Phonons and Kapitza Boundaries %D 1980 %T Stability of nonequilibrium superconducting states II : Theory and Experiments %A A.-M. S. Tremblay %E K.E. Gray %B NATO Advanced Study Institute on Nonequilibrium Superconductivity, Phonons and Kapitza Boundaries %V Proceedings of the NATO Advanced Study Institute on Nonequilibrium Superconductivity, Phonons and Kapitza Boundaries Chapter 11 %P 309-340 %8 1981 %0 Journal Article %J Journal of Physics A: General Physics %D 1980 %T Systematics of Carnot cycles at positive and negative Kelvin temperatures %A Landsberg, P.T. %A Tykodi, R.J. %A A.-M. S. Tremblay %B Journal of Physics A: General Physics %V 13 %P 1063-1074 %G eng %0 Journal Article %J Physical Review B %D 1979 %T Eigenmodes of the coupled two-dimensional Wigner-crystal-liquid-surface system and instability of a charged liquid surface %A A.-M. S. Tremblay %A Ambegaokar, V. %B Physical Review B %V 20 %P 2190-2195 %G eng %0 Journal Article %J Physical Review A %D 1979 %T Microscopic Calculation of the Nonlinear Current Fluctuations of a Metallic Resistor: the Problem of Heating in Perturbation Theory %A A.-M. S. Tremblay %A B.R. Patton %A F.C. Martin %A P.F. Maldague %B Physical Review A %V 19 %8 1979 %& 1721 %0 Journal Article %J Physical Review Letters %D 1979 %T Nonequilibrium Superconducting States with Two Coexisting Energy Gaps %A Gerd Schön %A A.-M. S. Tremblay %B Physical Review Letters %V 42 %8 1979 %& 1086 %0 Conference Proceedings %B Inhomogeneous Superconductors Conference %D 1979 %T Tunnel Injection Induced Nonequilibrium Superconducting States with two Coexisting Energy Gaps %A A.-M. S. Tremblay %A Gerd Schön %E D.U. Gubser %E T.L. Francavilla %E J.R. Leibowitz %E S.A. Wolf %B Inhomogeneous Superconductors Conference %S American Institute of Physics Conference Proceedings, Berkeley Springs %V Berkeley Springs # 58 %P 319-324 %8 1980 %0 Journal Article %J American Journal of Physics %D 1976 %T Comment on : Negative Kelvin Temperatures : Some Anomalies and a Speculation %A A.-M. S. Tremblay %B American Journal of Physics %V 44 %8 1976 %& 994 %0 Journal Article %J Physical Review B %D 1975 %T Nonadditive forces and vacancies in rare-gas crystals %A A.-M. S. Tremblay %A Glyde, H.R. %B Physical Review B %V 11 %P 1728-1731 %G eng