Effective action approach to strongly correlated fermion systems

TL;DR

This paper introduces a new functional for the single particle Green's function that extends dynamical mean field theory to finite-dimensional systems and links stationary solutions to physical phenomena like the Mott transition.

Contribution

A novel functional for the Green's function is developed, enabling direct derivation of DMFT equations and their extension to finite dimensions.

Findings

Functional stability relates to particle-hole interactions.

Extension of DMFT to finite dimensions.

Detection of Mott transition via bifurcation analysis.

Abstract

We construct a new 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 new 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 new 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 t o physical quantities resulting in divergences at the transition.