Effective-action approach to strongly correlated fermion systems

We construct a functional for the single-particle Green's function, which is a variant of the standard Baym-Kadanoff functional. The stability of the stationary solutions to the functional is directly related to aspects of the irreducible particle hole interaction through the Bethe-Salpeter equation. A startling aspect of this functional is that it allows a simple and rigorous derivation of both the standard and extended dynamical mean-field (DMFT) equations as stationary conditions. Though the DMFT equations were formerly obtained only in the limit of infinite lattice coordination, the functional described in the work presents a way of directly extending DMFT to finite-dimensional systems, both on a lattice and in a continuum. Instabilities of the stationary solution at the bifurcation point of the functional signal the appearance of a zero mode at the Mott transition which then couples to physical quantities resulting in divergences at the transition.