Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model

We analyze the occurrence of divergences in the irreducible vertex functions of the Anderson impurity model (AIM) [1]. These divergences — a surprising hallmark of the breakdown of many-electron perturbation theory [2] — have been recently observed [3,4] in several contexts, including the dynamical mean-field solution of the Hubbard model. Hitherto, however, a clarification of their origin could be obtained only in the limit of high temperatures and/or large interactions, where the
underlying physics is greatly simplified by the absence of low-energy quasiparticle excitations. In this respect, our numerical calculations for the AIM, as well as their comparison with the corresponding results for the Hubbard model, allow us to clarify several open questions about the origin and the properties of vertex divergences occurring in a more interesting context, the correlated metallic regime at low-temperatures.

[1] P. Chalupa, et.al., Phys. Rev. B 97, 245136 (2018).
[2] O. Gunnarsson, et.al., Phys. Rev. Lett. 119, 056402 (2017).
[3] T. Schäfer, et.al., Phys. Rev. Lett. 110, 246405 (2013).
[4] T. Schäfer, et.al., Phys. Rev. B 94, 235108 (2016).