Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom

Abstract

The local two-particle Green's function and its generalized susceptibility are central building blocks in state-of-the-art theoretical descriptions of strongly correlated many-electron systems. The unexpected discovery of singular points in the generalized susceptibility, resulting in divergences of the two-particle irreducible vertex function and in multivaluedness of the Luttinger-Ward functional, has therefore attracted considerable interest. Unfortunately, almost no analytical results for irreducible vertices are available for correlated electrons. Here, the authors fill this gap by presenting fully analytical expressions for all irreducible vertex function of a simple, yet prototypical, correlated model, the single-orbital Hubbard atom. This gives highly relevant insights into the energy dependence of these functions.