# Biography: Narrative 2010

**Biography: **André-Marie Tremblay was born in Montreal, Quebec in 1953. He received his B.Sc. from the Université de Montréal in 1974 and his Ph.D. from M.I.T. in 1978. After working for two years as a Postdoctoral Researcher at Cornell University, Prof. Tremblay took a position as a Natural Sciences and Engineering Council of Canada (NSERC) University Research Fellow at the University of Sherbrooke. He held this fellowship from 1980 to 1988, the year in which he became full professor. During the academic year 1986-87 he returned to Cornell University for a sabbatical leave.

He became an Associate of the Canadian Institute for Advanced Research Superconductivity Program (now called the Quantum Materials Program) in 1988. He is now a fellow of this program. From 1991 to 1999 he was Director of the University's Centre de recherche en physique du solide (Solid State Physics Research Centre). Since January 2001, Prof. Tremblay has held the Canada Research Chair in Condensed Matter Physics at the Université de Sherbrooke. He was an invited researcher at Yale University during the fall of 2003.

**Prizes, honors: **André-Marie Tremblay was nominated as a Fellow of the Royal Society of Canada in November 2004. He also won the Canadian Association of Physicists - Centre de Recherches Mathématiques Prize in Theoretical and Mathematical Physics in 2001 and the Urgel-Archambault Prize from ACFAS in 2003. He held a Killam Fellowship from the Canada Council for the Arts in 1992-1994, a Steacie Fellowship from NSERC in 1987-1989, and he received the Herzberg Medal from the Canadian Association of Physicists in 1986.

**Significant grants: **Tremblay presently holds a Discovery Grant from NSERC ($340,000 total, 2009-2014) a Canada Research Chair also from NSERC ($1,400,000 total, 2008-2015) and heads a team grant from the Government of Québec ($228 000 total, 2007-2011). He is a co-investigator for several major infrastructure grants and Canadian and Québec group grants. He is director of the Centre de Calcul Scientifique (Mammouth) in Sherbrooke.

**Main research achievements: **His thesis work was on the application of Quantum Field Theoretical methods to nonequilibrium Statistical Mechanics and in particular to the problem of nonequilibrium superconductivity and of 1/f noise. As a postdoc in 1978 he published on non-gaussian statistics of noise, electrons on helium, non-equilibrium superconductivity. He was asked to write a review on the latter subject. His best known contribution of that period was on fluctuations about simple non-equilibrium steady states where he showed how the Langevin formalism could be applied in steady-states. He was asked to write a review on this problem in 1984.

As a Faculty in Sherbrooke, beginning in 1980, his first work on fluctuations in dissipative steady-states of thin metallic films inspired the thesis work of Michael Roukes, who became later a leader in the field of mesoscopic physics. He also applied real space renormalization group methods to amphiphilic molecules of biological interest and to disordered systems, particularly to fractals and percolation. It is upon studying electrical noise on fractals and percolation clusters that he independently discovered, with Rammal, the concept of multifractals. This revolutionized thinking on critical exponents since multifractals lead to an infinite hierarchy of exponents, by contrast with the case encountered in critical phenomena where only a few exponents are relevant.

Although Tremblay continued to work on multifractals for several years after that, the discovery of the high-temperature superconductors during his sabbatical leave at Cornell in 1987 changed the course of his research. That year, high temperature superconductivity was discovered. It lay at the frontier of Condensed Matter Physics. The core of the problem consists in finding ways to treat electrons on a lattice when band and potential energy are comparable. The so-called Hubbard model embodies this physics. Encouraged by the fact that his colleagues at Sherbrooke worked on related problems and by his nomination as a member of the newly founded program of the Canadian Institute of Advanced Research on Superconductivity he embarked on a long term research program in this highly competitive field with the goal of finding non-perturbative theoretical approaches to that problem. Since it does not use perturbation theory, the approach that he developed allows one to treat the case where the kinetic energy of electrons is comparable to the potential energy, as found in high temperature superconductors. This analytical approach has been benchmarked against accurate numerical results and gives the best quantitative agreement with these. This new method is now known in literature as Two-Particle Self-Consistent (TPSC). The formal version of its derivation has allowed his team to extend it in many directions, including competition with ferromagnetism, pseudogap, attractive model, *d*-wave superconductivity and longer-range interactions. TPSC also provides quantitative estimates of the range of temperature where quantum critical behavior can be observed experimentally. Section 6.4.4 in the 3^{rd} edition of the influential textbook of G.D. Mahan is now devoted to TPSC. In a 2004 paper, heused TPSC to obtain agreement between theory, photoemission and neutron experiments in electron-doped cuprates. The predicted pseudogap temperature T^{*}, and scaling of the antiferromagnetic correlation length with the thermal de Broglie wavelength at T^{* }have both beenverified subsequently**.** The agreement with previous measurements and the accuracy of the predictions are unprecedented in the field. A large number of experimental results in electron-doped cuprates in the optimally doped and slightly underdoped regime find their natural explanation with his approach: The negative pressure dependence of Tc, the measurement of long AFM correlations and the appearance of the concomitant pseudogap with three Fermi arcs. His group has also studied the competition between antiferromagnetism and d-wave superconductivity. The d-wave superconducting transition found with TPSC agrees with Quantum Cluster approaches and with high-temperature simulation data, giving one of the strongest arguments in favor of the existence of superconductivity in the Hubbard model at weak to intermediate coupling, an issue that has been hotly debated. The approach also clarifies the conditions for the appearance of d-wave and the competing role of the pseudogap. He was invited to write a review on these topics in 2006, and in 2010 to write a Chapter on TPSC in a collective work.

Finally, using new numerical Quantum Cluster approaches that he helped develop, Tremblay’s group has performed large scale computer calculations that reproduce the doping range where antiferromagnetic and d-wave superconducting ground states occur in both the high-temperature superconductors and the BEDT organics. This is the first instance where such remarkable agreement with the observed ground states is obtained within the Hubbard model using the same method but for two different classes of materials. They have also been able to explain several anomalous properties of the superconducting phase.

**Dissemination of research results: **Tremblay has written over 140 papers, given 87 invited talks at conferences, his group has presented 180 contributed talks at meetings and he has given 160 talks at Universities or Government laboratories. He is on the Editorial board of Physical Review B since 2007 and has chaired numerous committees and organized workshops and summer schools on a regular basis.