Toulouse Points and Non-Fermi Liquid States in the Mixed Valence Regime of the Generalized Anderson Model

TL;DR

This paper identifies special points in a generalized Anderson impurity model where correlation functions can be exactly calculated, revealing both Fermi liquid and non-Fermi liquid behaviors in the mixed valence regime.

Contribution

The paper introduces the concept of Toulouse points in the mixed valence regime, providing exact solutions and revealing novel non-Fermi liquid phases.

Findings

Three Toulouse points with explicit correlation functions

Two points exhibit Fermi liquid behavior

One point shows spin-charge separation and non-Fermi liquid features

Abstract

We study the mixed valence regime of a generalized Anderson impurity model using the bosonization approach. This single impurity problem is defined by the $U=\infty$ Anderson model with an additional density-density interaction, as well as an explicit exchange interaction, between the impurity and conduction electrons. We find three points in the interaction parameter space at which all the correlation functions can be calculated explicitly. These points represent the mixed valence counterparts of the ususal Toulouse point for the Kondo problem, and are appropriately named the Toulouse points of the mixed valence problem. Two of the Toulouse points exhibit the strong coupling, Fermi liquid behavior. The third one shows spin-charge separation; here, the spin-spin correlation functions are Fermi-liquid-like, the charge-charge correlation functions and the single particle Green function have non-Fermi-liquid behaviors, and a pairing correlation function is enhanced compared to the Fermi liquid case. This third Toulouse point describes the novel intermediate mixed valence phase we have previously identified. In deriving these results, we emphasize the importance of keeping track of the anticommutation relation between the fermion fields when the bosonization method is applied to quantum impurity problems.