Abstract

Hedin’s equations provide an elegant route to compute the exact one-body Green’s function (or propagator) via the self-consistent iteration of a set of non-linear equations. Its first-order approximation, known as GW, corresponds to a resummation of ring diagrams and has shown to be extremely successful in physics and chemistry. Systematic improvement is possible, although challenging, via the introduction of vertex corrections. Considering anomalous propagators and an external pairing potential, we derive a new self-consistent set of closed equations equivalent to the famous Hedin equations but having as a first-order approximation the particle-particle (pp) T-matrix approximation where one performs a resummation of the ladder diagrams (known as the pp random phase approximation (RPA)). This pp version of Hedin’s equations offers a way to go systematically beyond the $T$-matrix approximation by accounting for low-order pp vertex corrections. In particular, we will show how to go beyond the pp-RPA-based T-matrix by formulating the Bethe-Salpeter equation for the two-particle propagator and discussing some of its approximations.