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)