It 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.

}, author = {Vilk, Y.M. and S. Allen and Touchette, H. and Moukouri, S. and Chen, L. and A.-M. S. Tremblay} } @article {Vilk:1994rv, title = {2-particle Self-consistent Theory For Spin and Charge Fluctuations In the Hubbard-model}, journal = {Physica C}, volume = {235}, year = {1994}, pages = {2235{\textendash}2236}, abstract = {A 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.

}, url = {http://www.sciencedirect.com/science/article/pii/0921453494923396}, author = {Vilk, Y.M. and Chen, L. and A.-M. S. Tremblay} } @article {Dare:1994kg, title = {Comparisons Between Monte-carlo Simulations and A Simple Crossing-symmetrical Approach To the Hubbard-model At Low-density}, journal = {Physical Review B}, volume = {49}, number = {6}, year = {1994}, pages = {4106{\textendash}4118}, abstract = {A 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.

}, author = {Dar{\'e}, A. M. and Chen, L. and A.-M. S. Tremblay} } @article {Dare:1994tl, title = {Correlation-functions of the Hubbard-model At Low-density In A Crossing-symmetrical Approximation - Comparisons With Monte-carlo Simulations}, journal = {Physica B}, volume = {194}, year = {1994}, pages = {1413{\textendash}1414}, abstract = {The 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.

}, author = {Dar{\'e}, A. M. and Chen, L. and A.-M. S. Tremblay} } @proceedings {7560, title = {Quantum Monte Carlo simulations for a model of high-tem{\textlnot}perature superconductors: effect of next-nearest-neighbor hopping}, volume = {University of Toronto Press}, year = {1994}, month = {1994}, pages = {78-85}, author = {Veilleux, A. F. and Dar{\'e}, A.-M. and Chen, L. and Vilk, Y.M. and A.-M. S. Tremblay}, editor = {John W. Ross} } @article {Vilk:1994hn, title = {Theory of Spin and Charge Fluctuations In the Hubbard-model}, journal = {Physical Review B}, volume = {49}, number = {18}, year = {1994}, pages = {13267{\textendash}13270}, abstract = {A 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.

}, author = {Vilk, Y.M. and Chen, L. and A.-M. S. Tremblay} } @article {Chen:1993er, title = {Flux-quantization In Rings For Hubbard (attractive and Repulsive) and T-j-like Hamiltonians - Comment}, journal = {Physical Review B}, volume = {47}, number = {22}, year = {1993}, pages = {15316{\textendash}15318}, abstract = {It 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.

}, author = {Chen, L. and Mei, C. J. and A.-M. S. Tremblay} } @article {Benard:1993nk, title = {Magnetic Neutron-scattering From 2-dimensional Lattice Electrons - the Case of La2-xsrxcuo4}, journal = {Physical Review B}, volume = {47}, number = {22}, year = {1993}, pages = {15217{\textendash}15241}, abstract = {It 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.

}, author = {B{\'e}nard, P. and Chen, L. and A.-M. S. Tremblay} } @article {Benard:1993sv, title = {Neutron-scattering Measurements As A Test of Theories of High-temperature Superconductivity}, journal = {Physical Review B}, volume = {47}, number = {1}, year = {1993}, pages = {589{\textendash}592}, abstract = {It 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.

}, author = {B{\'e}nard, P. and Chen, L. and A.-M. S. Tremblay} } @article {Chen:1992tz, title = {Determinant Monte-carlo For the Hubbard-model With Arbitrarily Gauged Auxiliary Fields}, journal = {International Journal of Modern Physics B}, volume = {6}, number = {5-6}, year = {1992}, pages = {547{\textendash}560}, abstract = {Monte 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.

}, url = {https://www.worldscientific.com/doi/abs/10.1142/S0217979292000323}, author = {Chen, L. and A.-M. S. Tremblay} } @conference {7579, title = {The influence of spin fluctuations on the temperature dependance of the magnetic susceptibility and nuclear relaxation in high Tc superconductors}, booktitle = {10th Specialized Colloque AMPERE, NMR/NQR in High-Tc Superconductors}, year = {1991}, month = {08/1991}, address = {Zurich, Suisse}, author = {T.W. Li and C Bourbonnais and Chen, L. and A.-M. S. Tremblay}, editor = {D. Brinkmann} } @article {Chen:1991ap, title = {Magnetic-properties of the 2-dimensional Hubbard-model}, journal = {Physical Review Letters}, volume = {66}, number = {3}, year = {1991}, pages = {369{\textendash}372}, abstract = {Monte 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.

}, author = {Chen, L. and C Bourbonnais and Li, T. and A.-M. S. Tremblay} } @proceedings {7559, title = {Monte Carlo Method for Strongly Interacting Electrons}, volume = {Proceedings of Supercomputing Symposium {\textquoteright}90}, year = {1990}, month = {1990}, pages = {197-210}, address = {Montr{\'e}al}, author = {A.-M. S. Tremblay and C. Boily and Chen, L. and Nelisse, H. and Reid, A.}, editor = {Dominique Pelletier} }