Stability bounds for the generalized Kadanoff-Baym ansatz in the Holstein dimer

TL;DR

This paper investigates the stability of the Generalized Kadanoff-Baym Ansatz (GKBA) in simulating electron-phonon dynamics within the Holstein dimer, providing practical bounds and diagnostics for reliable use.

Contribution

It identifies parameter regions where GKBA remains stable or fails in the Holstein dimer, and offers guidelines to improve its reliability in electron-phonon simulations.

Findings

GKBA stability depends on system parameters and ground-state properties.

Coupling to electronic leads can mitigate GKBA instabilities.

The paper provides practical diagnostics for GKBA reliability.

Abstract

Predicting real-time dynamics in correlated systems is demanding: exact two-time Green's function methods are accurate but often too costly, while the Generalized Kadanoff-Baym Ansatz (GKBA) offers time-linear propagation at the risk of uncontrolled behavior. We examine when and why GKBA fails in a minimal yet informative setting, the Holstein dimer that describes electron-phonon coupling. Using a conserving, fully self-consistent electron-phonon self-energy, we map out parameter regions where GKBA dynamics is stable and where it becomes unstable. We trace the onset of these failures to qualitative changes in the model's ground-state solutions obtained from the full nonequilibrium Green's function theory, thereby providing practical stability bounds for GKBA time evolution. We further show that coupling the dimer to electronic leads can damp and, in part, cure these instabilities. The results supply simple diagnostics and guidelines for reliable GKBA simulations of electron-phonon dynamics.