Generalization of correlated electron-ion dynamics from nonequilibrium Green's functions

TL;DR

This paper introduces a generalized formulation of correlated electron-ion dynamics (CEID) using nonequilibrium Green's functions, connecting it with diagrammatic perturbation theory and comparing it with the self-consistent Born approximation.

Contribution

It extends CEID to nonequilibrium ensembles with variable electron number and establishes a rigorous connection with diagrammatic perturbation theory, enabling systematic improvements.

Findings

CEID and SCBA coincide at weak electron-phonon coupling.

CEID and SCBA differ in the large ionic mass limit.

The relation between CEID and SCBA is illustrated through fourth-order perturbation theory.

Abstract

We present a new formulation of the correlated electron-ion dynamics (CEID) by using equations of motion for nonequilibrium Green's functions, which generalizes CEID to a general nonequilibrium statistical ensemble that allows for a variable total number of electrons. We make a rigorous connection between CEID and diagrammatic perturbation theory, which furthermore allows the key approximations in CEID to be quantified in diagrammatic terms, and, in principle, improved. We compare analytically the limiting behavior of CEID and the self-consistent Born approximation (SCBA) for a general dynamical nonequilibrium state. This comparison shows that CEID and SCBA coincide in the weak electron-phonon coupling limit, while they differ in the large ionic mass limit where we can readily quantify their difference. In particular, we illustrate the relation between CEID and SCBA by perturbation theory at the fourth-order in the coupling strength.