Diagrammatic theory of the irreducible coupled-cluster self-energy

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), <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>G</a:mi><a:mi>W</a:mi></a:mrow></a:math>-BSE, and CC theory for ground state and excitation energies. This clarifies the origin of previously established connections between RPA, <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>G</b:mi><b:mi>W</b:mi></b:mrow></b:math>-BSE, and CC theory, and it exposes the relationship between vertex corrections and the coupled-cluster amplitude equations.