Diagrammatic theory of the irreducible coupled-cluster self-energy

TL;DR

This paper introduces a diagrammatic framework that unifies coupled-cluster theory with many-body Green's function methods, clarifying their interconnections and providing a comprehensive approach to electron correlation.

Contribution

It presents a diagrammatic definition of the irreducible coupled-cluster self-energy that embeds CC theory within many-body field theory, unifying RPA, GW-BSE, and CC approaches.

Findings

Unified description of RPA, GW-BSE, and CC theories.

Clarified the relationship between vertex corrections and CC amplitude equations.

Provided a diagrammatic foundation for coupled-cluster self-energy.

Abstract

Coupled-cluster and Green's function theories are highly successful in treating many-body electron correlation, and there has been significant interest in identifying and leveraging connections between them. Here we present a diagrammatic definition of the irreducible coupled-cluster self-energy that directly embeds coupled-cluster (CC) theory within the framework of many-body field theory. The equation-of-motion coupled-cluster (EOM-CC) treatment emerges naturally from our definition via the Dyson equation and the Bethe-Salpeter equation (BSE), providing a unified description of the random phase approximation (RPA), $GW$-BSE, and CC theory for ground state and excitation energies. This clarifies the origin of previously established connections between RPA, $GW$-BSE, and CC theory, and it exposes the relationship between vertex corrections and the coupled-cluster amplitude equations.