Nonequilibrium perturbation theory of the spinless Falicov-Kimball model

TL;DR

This paper develops a second-order perturbation theory for nonequilibrium Green functions in the spinless Falicov-Kimball model under an electric field, revealing limitations in reaching steady state at long times.

Contribution

It introduces a truncated second-order perturbative approach for nonequilibrium Green functions in the model, highlighting its limitations in long-time behavior.

Findings

Perturbation theory fails to reach steady state at long times.

Pathological behavior observed for times greater than 2/U.

Comparison with Boltzmann and exact solutions shows limitations of the approach.

Abstract

We perform a perturbative analysis for the nonequilibrium Green functions of the spinless Falicov-Kimball model in the presence of an arbitrary external time-dependent but spatially uniform electric field. The conduction electron self-energy is found from a strictly truncated second-order perturbative expansion in the local electron-electron repulsion U. We examine the current at half-filling, and compare to both the semiclassical Boltzmann equation and exact numerical solutions for the contour-ordered Green functions from a transient-response formalism (in infinite dimensions) on the Kadanoff-Baym-Keldysh contour. We find a strictly truncated perturbation theory in the two-time formalism cannot reach the long-time limit of the steady state; instead it illustrates pathological behavior for times larger than approximately 2/U.