Nonequilibrium dynamical mean-field theory of strongly correlated electrons

TL;DR

This paper reviews the extension of dynamical mean-field theory to nonequilibrium situations, focusing on electric field effects in strongly correlated electrons, and compares numerical methods for solving these complex systems.

Contribution

It introduces a gauge-invariant formalism for nonequilibrium DMFT and applies it to the Falicov-Kimball model, illustrating behavior in metals and insulators.

Findings

Demonstrates nonequilibrium behavior in diffusive metals and Mott insulators

Compares numerical approaches like transient-response formalism and perturbation theory

Provides a framework for studying time-dependent electric fields in correlated systems

Abstract

We present a review of our recent work in extending the successful dynamical mean-field theory from the equilibrium case to nonequilibrium cases. In particular, we focus on the problem of turning on a spatially uniform, but possibly time varying, electric field (neglecting all magnetic field effects). We show how to work with a manifestly gauge-invariant formalism, and compare numerical calculations from a transient-response formalism to different types of approximate treatments, including the semiclassical Boltzmann equation and perturbation theory in the interaction. In this review, we solve the nonequilibrium problem for the Falicov-Kimball model, which is the simplest many-body model and the easiest problem to illustrate the nonequilibrium behavior in both diffusive metals and Mott insulators. Due to space restrictions, we assume the reader already has some familiarity both with the Kadanoff-Baym-Keldysh nonequilibrium formalism and with equilibrium dynamical mean-field theory; we provide a guide to the literature where additional details can be found.