Thermodynamically consistent description of criticality in models of correlated electrons

TL;DR

This paper develops a diagrammatic approach ensuring consistent symmetry breaking in one- and two-particle functions, accurately capturing quantum critical behavior in correlated electron models like the Anderson model.

Contribution

It introduces a general scheme for two-particle approximations that align with one-particle functions, enabling consistent descriptions of criticality in correlated electron systems.

Findings

Successfully applied to the Anderson model

Reproduces the Kondo critical scale from spectral and magnetic data

Ensures qualitative agreement between different thermodynamic descriptions

Abstract

Criticality in models of correlated electrons emerges in proximity of a low-temperature singularity in a two-particle Green function. Such singularities are generally related to a symmetry breaking of the one-particle self-energy. A consistent description demands that the symmetry breaking in the self-energy emerges at the critical point of the respective two-particle function. This cannot easily be achieved in models of correlated electrons, since there are two ways connecting one- and two-electron functions that cannot be made fully equivalent in approximations. We present a general construction of diagrammatic two-particle approximations consistent with the one-particle functions so that both produce qualitatively the same quantum critical behavior in thermodynamically equivalent descriptions. The general scheme is applied on the single-impurity Anderson model to derive qualitatively the same Kondo critical scale from the spectral function and the magnetic susceptibility.