Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields

TL;DR

This paper derives exact spectral moment sum rules for nonequilibrium Green's functions in strongly correlated electron models under time-dependent electric fields, aiding numerical accuracy assessment.

Contribution

It extends spectral moment sum rules to nonequilibrium conditions in the Falicov-Kimball and Hubbard models, providing a theoretical basis for numerical validation.

Findings

Derived exact expressions for spectral moments in nonequilibrium.

Compared theoretical sum rules with numerical solutions, confirming their accuracy.

Enabled improved estimation of numerical calculation errors in strongly correlated systems.

Abstract

We derive exact operator average expressions for the first two spectral moments of nonequilibrium Green's functions for the Falicov-Kimball model and the Hubbard model in the presence of a spatially uniform, time-dependent electric field. The moments are similar to the well-known moments in equilibrium, but we extend those results to systems in arbitrary time-dependent electric fields. Moment sum rules can be employed to estimate the accuracy of numerical calculations; we compare our theoretical results to numerical calculations for the nonequilibrium dynamical mean-field theory solution of the Falicov-Kimball model at half-filling.