Interacting electrons and bosons in the doubly screened $G\widetilde{W}$ approximation: A time-linear scaling method for first-principles simulations

TL;DR

This paper introduces a versatile, linearly scaling first-principles simulation method combining electron and boson interactions using the $G ilde{W}$ approximation, enabling efficient and accurate modeling of complex correlated systems.

Contribution

It develops a time-linear scaling framework incorporating the $G ilde{W}$ approximation for electrons and bosons, allowing multiple correlation effects to be included simultaneously.

Findings

Demonstrates improved accuracy over existing methods in charge migration simulations.

Provides a flexible diagrammatic approach with 2^{12} methods.

Ensures conservation laws are preserved in all simulations.

Abstract

We augment the time-linear formulation of the Kadanoff-Baym equations for systems of interacting electrons and quantized phonons or photons with the $G\widetilde{W}$ approximation, the Coulomb interaction $\widetilde{W}$ being dynamically screened by both electron-hole pairs {\em and} bosonic particles. We also show how to combine different approximations to include simultaneously multiple correlation effects in the dynamics. The final outcome is a versatile framework comprising $2^{12}$ distinct diagrammatic methods, each scaling linearly in time and preserving all fundamental conservation laws. The dramatic improvement over current state-of-the-art approximations brought about by $G\widetilde{W}$ is demonstrated in a study of the correlation-induced charge migration of the glycine molecule in an optical cavity.