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

TL;DR

This paper investigates divergences in irreducible vertex functions within the Anderson Impurity Model, clarifying their origin, relation to Kondo physics, and implications for correlated metallic systems at low temperatures.

Contribution

It provides a detailed analysis of vertex divergences in the AIM, clarifying their connection to charge fluctuations, Kondo physics, and potential real-frequency manifestations, advancing understanding of many-body perturbation breakdowns.

Findings

Vertex divergences are not necessarily linked to a Mott transition.

Divergences relate to the suppression of charge fluctuations.

Scaling properties suggest some divergences may appear on the real frequency axis.

Abstract

In this work, we analyze in detail the occurrence of divergences in the irreducible vertex functions for one of the fundamental models of many-body physics: the Anderson impurity model (AIM). These divergences -- a surprising hallmark of the breakdown of many-electron perturbation theory -- have been recently observed in several contexts, including the dynamical mean-field solution of the Hubbard model. The numerical calculations for the AIM presented in this work, 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 in a particularly interesting context, the correlated metallic regime at low-temperatures. Specifically, our analysis (i) rules out explicitly the transition to a Mott insulating phase, but not the more general suppression of charge fluctuations (proposed in [Phys.\,Rev.\,B {\bf 93},\,245102\,(2016)]), as a necessary condition for the occurrence of vertex divergences, (ii) clarifies their relation with the underlying Kondo physics, and, eventually, (iii) individuates which divergences might also appear on the real frequency axis in the limit of zero temperature, through the discovered scaling properties of the singular eigenvectors.