The breakdown of self-consistent perturbation theory for many-electron systems manifests itself in several ways. Among the most studied mathematical manifestations are (i) the divergence of two-particle irreducible vertex functions and (ii) the multivaluedness of the Luttinger Ward functional.

Up to now, most investigations of the perturbation theory breakdown in many-electron models have been restricted to particle-hole symmetric models at nonzero temperature. We take a first step beyond this by investigating the two-particle properties of the Hubbard Atom, both for positive (repulsive) and negative (attractive) on-site interaction.

As a main result a universal phase diagram of vertex divergences at arbitrary (finite) temperatures is determined. Using this finding as a “compass”, the T=0 limit will be investigated, in order to unveil possible connections between the vertex divergences and the validity or the violation of the Luttinger Theorem. Finally, we analyze the self-consistent perturbation series beyond the particle-hole symmetry condition, searching for specific constraints for its convergence of to a physical solution.