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

TL;DR

This paper establishes a formal connection between the electronic self-energy and coupled-cluster doubles theory, deriving amplitude equations and correlation energy expressions, and demonstrating their validity through the Hubbard dimer model.

Contribution

It introduces a novel derivation of CCD amplitude equations via the particle-hole-time decoupled self-energy, linking it to established EOM-CCD methods.

Findings

Derived CCD amplitude equations from self-energy formalism

Expressed ground state correlation energy in CCD form

Validated the formalism with exact Hubbard dimer solution

Abstract

We derive the coupled-cluster doubles (CCD) amplitude equations by introduction of the particle-hole-time decoupled electronic self-energy. The resulting analysis leads to an expression for the ground state correlation energy that is exactly of the form obtained in coupled-cluster doubles theory. We demonstrate the relationship to the ionization potential/electron affinity equation-of-motion coupled-cluster doubles (IP/EA-EOM-CCD) eigenvalue problem by coupling the reverse-time self-energy contributions while maintaining particle-hole separability. The formal relationships established are demonstrated by exact solution of the Hubbard dimer.