Connections between many-body perturbation and coupled-cluster theories

TL;DR

This paper establishes formal connections between many-body perturbation theory (GW and Bethe-Salpeter equations) and coupled-cluster theory, enabling transfer of methods and insights between these approaches for computing ground and excited states.

Contribution

It recasts GW and Bethe-Salpeter equations as non-linear coupled-cluster-like equations, bridging the two theoretical frameworks and facilitating method transfer.

Findings

Recasting GW and BSE as CC-like equations.

Identifying similarities with the similarity-transformed EOM-CC method.

Potential for computing ground- and excited-state properties within GW and BSE.

Abstract

Here, we build on the works of Scuseria (et al.) http://dx.doi.org/10.1063/1.3043729 and Berkelbach https://doi.org/10.1063/1.5032314 to show connections between the Bethe-Salpeter equation (BSE) formalism combined with the $GW$ approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the $GW$ and Bethe-Salpeter equations as non-linear CC-like equations. Similitudes between BSE@$GW$ and the similarity-transformed equation-of-motion CC method introduced by Nooijen are also put forward. The present work allows to easily transfer key developments and general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the $GW$ and BSE frameworks.