Anderson-Yuval approach to the multichannel Kondo problem

TL;DR

This paper extends the Anderson-Yuval technique to analyze the multichannel Kondo model with anisotropic couplings and magnetic field, providing insights into non-Fermi liquid to Fermi liquid crossover.

Contribution

It generalizes the Anderson-Yuval approach to multichannel Kondo models with anisotropy and magnetic field, and maps the two-channel case onto a solvable resonant level model.

Findings

Mapped two-channel Kondo model to a generalized resonant level model.

Identified solvable limiting cases of the resonant level model.

Described the crossover from non-Fermi liquid to Fermi liquid behavior.

Abstract

We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval technique. For two channels, we are able to map the Kondo model onto a generalized resonant level model. Limiting cases in which the equivalent resonant level model is solvable are identified. The solution correctly captures the properties of the two channel Kondo model, and also allows an analytic description of the cross-over from the non Fermi liquid to the Fermi liquid behavior caused by the channel anisotropy.