Nonlinear response of Bloch electrons in infinite dimensions

TL;DR

This paper analyzes the exact nonlinear response of noninteracting Bloch electrons in infinite dimensions under time-varying electric fields, providing key Green's functions for studying strongly correlated systems.

Contribution

It presents a formalism for calculating the nonlinear response of Bloch electrons in infinite dimensions, including Green's functions and current, useful for nonequilibrium dynamical mean field theory.

Findings

Derived exact Green's functions for nonlinear response

Analyzed transient behavior under pulsed electric fields

Provided foundational input for strongly correlated electron studies

Abstract

The exact nonlinear response of noninteracting (Bloch) electrons is examined within a nonequilibrium formalism on the infinite-dimensional hypercubic lattice. We examine the effects of a spatially uniform, but time-varying electric field (ignoring magnetic-field effects). The electronic Green's functions, Wigner density of states, and time-varying current are all determined and analyzed. We study both constant and pulsed electric fields, focusing on the transient response region. These noninteracting Green's functions are an important input into nonequilibrium dynamical mean field theory for the nonlinear response of strongly correlated electrons.