Nonequilibrium spectral moment sum rules of the Holstein-Hubbard model

TL;DR

This paper develops a method to evaluate spectral moment sum rules for the Holstein-Hubbard model, useful for analyzing time-dependent phenomena and benchmarking numerical methods in many-body physics.

Contribution

It introduces a general procedure for calculating spectral moment sum rules in the Holstein-Hubbard model with arbitrary parameters and corrects previous errors in simpler models.

Findings

Derived sum rules for zeroth to third spectral moments of Green's function and self-energy.

Applicable to time-resolved spectroscopy and numerical benchmarking.

Provides momentum space sum rules for translationally invariant systems.

Abstract

We derive a general procedure for evaluating the ${\rm n}$th derivative of a time-dependent operator in the Heisenberg representation and employ this approach to calculate the zeroth to third spectral moment sum rules of the retarded electronic Green's function and self-energy for a system described by the Holstein-Hubbard model allowing for arbitrary spatial and time variation of all parameters (including spatially homogeneous electric fields and parameter quenches). For a translationally invariant (but time-dependent) Hamiltonian, we also provide sum rules in momentum space. The sum rules can be applied to various different phenomena like time-resolved angle-resolved photoemission spectroscopy and benchmarking the accuracy of numerical many-body calculations. This work also corrects some errors found in earlier work on simpler models.