Exact finite-size spectrum for the multi-channel Kondo model and Kac-Moody fusion rules

TL;DR

This paper analytically derives the exact finite-size spectrum for the multi-channel Kondo model, confirming the Kac-Moody fusion hypothesis and connecting Kondo scattering with RSOS models.

Contribution

It provides an exact analytical derivation of the finite-size spectrum for the multi-channel Kondo model using Kac-Moody fusion rules, specifically for the case n-2S=1.

Findings

Finite-size spectrum matches Kac-Moody fusion predictions.

Mapping Kondo scattering to RSOS models is successful.

Results confirm the Kac-Moody fusion hypothesis.

Abstract

The finite-size spectrum for the multi-channel Kondo model is derived analytically from the exact solution, by mapping the nontrivial Z$_{n}$ part of the Kondo scattering into that for the RSOS model coupled with the impurity. The analysis is performed for the case of $n-2S=1$, where $n$ is the number of channel and $S$ is the impurity spin. The result obtained is in accordance with the Kac-Moody fusion hypothesis proposed by Affleck and Ludwig.