Connection between $GW$ and Extended Coupled Cluster

TL;DR

This paper explores the formal connection between $GW$ approximation and coupled-cluster theory, proposing an extended CC framework that unifies these methods and enables systematic improvements in Green's function calculations.

Contribution

It introduces an extended coupled-cluster (ECC) approach that unifies CC and Green's function methods, allowing for vertex corrections and systematic improvements.

Findings

Establishes a formal link between $GW$ and CC theories.

Proposes an ECC framework for improved Green's function methods.

Enables systematic inclusion of vertex corrections within CC.

Abstract

Coupled-cluster (CC) theory and Green's function many-body perturbation theory (MBPT) have long evolved as distinct yet complementary frameworks for describing electronic correlation. While CC methods employ exponential wavefunction parametrizations that guarantee size extensivity and systematic improvability, Green's function approaches such as the $GW$ approximation describe quasiparticle and optical excitations through diagrammatic resummations. Recent analyses have established a formal correspondence between these frameworks: the $GW$ approximation is equivalent to an equation-of-motion (EOM) treatment of the direct-ring coupled-cluster doubles (drCCD) method. Within this context, the extended CC (ECC) ansatz offers a unified framework connecting CC and MBPT. This formulation bridges CC-based and Green's function-based methods, providing novel avenues for incorporating vertex corrections within a CC framework that keep a positive semi-definite self-energy and lead to potentially systematically improvable Green's function approaches.