Toulouse limit for the overscreened four-channel Kondo problem

TL;DR

This paper establishes a Toulouse limit for the four-channel Kondo model by mapping its spin dynamics to a model with a spin 1/2 impurity coupled to spin 1 conduction electrons, using abelian bosonization.

Contribution

It introduces a Toulouse limit for the four-channel Kondo problem, extending the known two-channel case and providing a new analytical approach.

Findings

Identifies an equivalence between the four-channel Kondo model and a spin 1/2 impurity in a spin 1 conduction electron environment.

Derives a Toulouse limit for the four-channel Kondo model using abelian bosonization.

Provides insights by relating the problem to impurity models in Luttinger liquids.

Abstract

We show that the spin dynamics of the 4--channel Kondo model is equivalent to the one of a model with a spin 1/2 impurity coupled to spin 1 conduction electrons. By abelian bosonization of the latter model we find a kind of Toulouse limit analogous to that recently discussed by Emery and Kivelson for the 2--channel case. We analyse the model by exploiting the close analogy to the problem of an impurity in the Luttinger liquid.