Diagrammatic theory of the irreducible 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.

References in corpus (18)

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• Efficient excitations and spectra within a perturbative renormalization approach
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• A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory
• Nonconvergence of the Feynman-Dyson diagrammatic perturbation expansion of propagators
• Constructing `full-frequency' spectra via moment constraints for coupled cluster Green's functions

Cited by in corpus (1)

• Uncovering relationships between the electronic self-energy and coupled-cluster doubles theory