Connections between many-body perturbation and coupled-cluster theories

Here, we build on the works of Scuseria et al. [J. Chem. Phys. 129, 231101 (2008)] and Berkelbach [J. Chem. Phys. 149, 041103 (2018)] 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 are also put forward. The present work allows us to easily transfer key developments and the 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. (C) 2022 Author(s).

Automated summary

Building on previous works, this study explores the connections between the Bethe-Salpeter equation (BSE) combined with the GW approximation and coupled-cluster (CC) theory at the ground- and excited-state levels. The authors demonstrate a method to transform the GW and Bethe-Salpeter equations into non-linear CC-like equations and highlight the similarities between BSE@GW and the similarity-transformed equation-of-motion CC method. This work enables the transfer of key developments and general knowledge from CC theory to many-body perturbation theory, specifically for computing ground- and excited-state properties within the GW and BSE frameworks.