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

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.

References in corpus (4)

• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Quenching Bloch oscillations in a strongly correlated material
• Nonequilibrium perturbation theory of the spinless Falicov-Kimball model
• Sum rules and vertex corrections for electron-phonon interactions

Cited by in corpus (5)

• Steady-state nonequilibrium density of states of driven strongly correlated lattice models in infinite dimensions
• Non-equilibrium cluster-perturbation theory
• Moment-functional based spectral density-functional theory
• Nonequilibrium sum rules for the Holstein model
• Nonequilibrium spectral moment sum rules of the Holstein-Hubbard model