Renormalization-group approach to interacting fermions coupled to phonons

Shan-Wen Tsai Boston University

Abstract: Electron-electron interactions are responsible for a vast number of striking phenomena in condensed matter systems. Electrons in solids also interact with bosonic modes, such as phonons. Experimental results show that in many strongly correlated systems, such as organic conductors and superconductors, charge-density-wave inorganics and high-temperature superconductors, both electron interactions and phonons may play an important role. In this talk I will present a functional renormalization-group method for treating both these interactions on an equal footing. The renormalization-group technique allows the study of the stability of the Fermi liquid state and its instabilities toward other competing phases, such as charge- and spin-density-wave states and superconductivity. When interactions with bosonic modes, such as phonons, are also present, the problem is profoundly affected by retardation effects and multiple energy scales, which have to be taken into account. I will discuss how this problem is solved with the renormalization-group method, how it leads, in a controlled way, to Migdal's theorem and Eliashberg's theory for superconductivity, and further applications of the method. The development of this technique opens new doors for treating systems of interacting fermions coupled with bosons, where several instabilities may be present and may compete or cooperate with each other. (References: cond-mat/0406174 and cond/mat/0505426)