Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons

TL;DR

This paper derives nonequilibrium sum rules for the retarded self-energy in strongly correlated electron models, providing a tool to test the accuracy of numerical solutions in nonequilibrium conditions.

Contribution

It extends the known sum rules to the retarded self-energy in the Falicov-Kimball and Hubbard models under time-dependent electric fields, including the third moment.

Findings

Self-energy sum rules are more accurately satisfied than Green's function sum rules.

Sum rules are validated for the Falicov-Kimball model in infinite dimensions.

The derived sum rules serve as benchmarks for nonequilibrium many-body calculations.

Abstract

We derive the first two moment sum rules of the conduction electron retarded self-energy for both the Falicov-Kimball model and the Hubbard model coupled to an external spatially uniform and time-dependent electric field (this derivation also extends the known nonequilibrium moment sum rules for the Green's functions to the third moment). These sum rules are used to further test the accuracy of nonequilibrium solutions to the many-body problem; for example, we illustrate how well the self-energy sum rules are satisfied for the Falicov-Kimball model in infinite dimensions and placed in a uniform electric field turned on at time t=0. In general, the self-energy sum rules are satisfied to a significantly higher accuracy than the Green's functions sum rules.