Universality class of non-Fermi liquid behavior in mixed valence systems

TL;DR

This paper derives an exactly solvable model for mixed valence systems, revealing a new non-Fermi liquid behavior at quantum criticality characterized by unusual temperature dependencies in specific heat and susceptibility.

Contribution

It introduces a generalized Anderson impurity model with off-site Coulomb interactions, solving it in the strong coupling limit and predicting novel non-Fermi liquid behavior at the quantum critical point.

Findings

Discovery of a mixed valence quantum critical point separating two Fermi liquid phases.

Prediction of non-Fermi liquid behavior with specific heat ~ T^{1/4} and susceptibility ~ T^{-3/4}.

Application of the model to explain experimental observations in UPd_xCu_{5-x} alloys.

Abstract

A generalized Anderson single-impurity model with off-site Coulomb interactions is derived from the extended three-band Hubbard model, originally proposed to describe the physics of the copper-oxides. Using the abelian bosonization technique and canonical transformations, an effective Hamiltonian is derived in the strong coupling limit, which is essentially analogous to the Toulouse limit of the ordinary Kondo problem. In this limit, the effective Hamiltonian can be exactly solved, with a mixed valence quantum critical point separating two different Fermi liquid phases, {\it i.e.} the Kondo phase and the empty orbital phase. In the mixed valence quantum critical regime, the local moment is only partially quenched and X-ray edge singularities are generated. Around the quantum critical point, a new type of non-Fermi liquid behavior is predicted with an extra specific heat $C_{imp}\sim T^{1/4}$ and a singular spin-susceptibility $\chi_{imp}\sim T^{-3/4}$. At the same time, the effective Hamiltonian under single occupancy is transformed into a resonant-level model, from which the correct Kondo physical properties (specific heat, spin susceptibility, and an enhanced Wilson ratio) are easily rederived. Finally, a brief discussion is given to relate these theoretical results to observations in $UPd_xCu_{5-x}$ ($x=1,1.5$) alloys, which show single-impurity critical behavior consistent with our predictions.