Impurity problems for steady-state nonequilibrium dynamical mean-field theory

TL;DR

This paper develops a detailed theoretical framework for impurity problems in steady-state nonequilibrium dynamical mean-field theory, focusing on current flow under electric fields and applicable to models like Falicov-Kimball and Hubbard.

Contribution

It provides an exact formalism for impurity problems in nonequilibrium DMFT, including path integral formulation and Green's function dependence, extending to complex models.

Findings

Exact formalism for Falicov-Kimball model

Modified formalism for Hubbard model

Detailed mapping of lattice to impurity in nonequilibrium

Abstract

The mapping of steady-state nonequilibrium dynamical mean-field theory from the lattice to the impurity is described in detail. Our focus is on the case with current flow under a constant dc electric field of arbitrary magnitude. In addition to formulating the problem via path integrals and functional derivatives, we also describe the distribution function dependence of the retarded and advanced Green's functions. Our formal developments are exact for the Falicov-Kimball model. We also show how these formal developments are modified for more complicated models (like the Hubbard model).