The recently discovered occurrence of multiple divergences in the irreducible vertex functions of strongly correlated electron models, poses serious problems to the stateoftheart manybody theory. Dynamical meanfield theory (DMFT) calculations for the Hubbard model have shown several lines of divergences of the irreducible vertex function, surrounding the MottHubbard metalinsulator transition, a clear hint of a highly nonperturbative origin. At high temperatures/large interaction (U), where the Hubbard model approaches the atomic limit, the divergences could be ascribed to a unique underlying energy scale . This simple picture is however not applicable in the most interesting parameter regime of low temperatures and intermediate U, where the system behaves like a correlated Fermiliquid metal. For this reason a simpler model was analysed, where a similar physics could be realized: the Anderson impurity model. ^This provides a more feasible way to treat the Fermiliquid quasiparticle physics in the parameter regime of interest. In a preceding Projektarbeit I performed CTHYB calculations at the two particle level, using w2dynamics. The results show the first divergence line for the Anderson impurity model, with an unexpected low temperature behaviour. Motivated by these preliminary findings, in this thesis an investigation of the whole phase diagram of the Anderson impurity model has been per formed. In particular, using w2dynamics, additional lines of divergences were found: They could be classified in terms of the properties of their associated singular eigenvectors and compared with the corresponding ones found in other manyelectron systems. ^This information provides novel insights on the physical mechanism underlying the breakdown of manybody perturbation theory, clarifying some aspects (such as the relation of the divergences with the MottHubbard transition), which were not fully understood yet. In the final part of the master thesis the implication of the lowtemperature behaviour of the divergence lines in the Anderson impurity model onto other models (such as the Hubbard) is discussed as well.
