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arXiv:2210.07043 · The Journal of Chemical Physics

Connections between many-body perturbation and coupled-cluster theories

Raúl Quintero-Monsebaiz, Enzo Monino, Antoine Marie, Pierre‐François Loos

Published Nov 28, 2022• 28 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/5.0130837

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This dissertation deals with aspects of many-body problem in the electronic structure of solids. More specifically, we study how the introduction of Green’s function of many bodies and their equation of motion leads to information about the interactions between particles. Thus, we get to the GW and Bethe-Salpeter formalisms. We show in specific cases how the GW is able to describe energy gaps at a level that goes beyond the Density Functional Theory. Likewise, we investigate the inclusion of excitonic effects through the Bethe-Salpeter equation, showing how the approach can provide optical spectra in good agreement with experimental results. We exemplify the above points with the discussion of specific cases.