Kondo effect in a Luttinger liquid: nonuniversality of the Wilson ratio

TL;DR

This paper investigates how electron backscattering affects the Kondo effect in a Luttinger liquid, revealing nonuniversality in the Wilson ratio and identifying a new fixed point through a coset Ising-Bose approach.

Contribution

It introduces a coset Ising-Bose representation to analyze the destabilization of the two-channel Kondo fixed point by backscattering, showing the nonuniversality of the Wilson ratio.

Findings

Backscattering destabilizes the two-channel Kondo fixed point.

The Wilson ratio is not well-defined in the spinon basis with backscattering.

A new fixed point consistent with previous results is identified.

Abstract

Using a precise coset Ising-Bose representation, we show how backscattering of electrons off a magnetic impurity destabilizes the two-channel Kondo fixed point and drives the system to a new fixed point, in agreement with previous results. In addition, we verify the scaling proposed by Furusaki and Nagaosa and prove that the other possible critical fixed point, namely the local Fermi liquid class, is not completely universal when backscattering is included because the Wilson ratio is not well-defined in the spinon basis.