The Toulose limit of the Multi-Channel Kondo model.

TL;DR

This paper investigates the Toulouse limit of the multi-channel Kondo model, revealing that for more than two channels, the model remains non-trivial, with significant simplifications only at two channels.

Contribution

It identifies the conditions under which the Toulouse limit remains non-trivial for multi-channel Kondo models and clarifies the special case of two channels.

Findings

For more than two channels, interactions do not vanish at the Toulouse limit.

The model remains a non-trivial field theory beyond two channels.

Bethe ansatz reproduces known results specifically for two channels.

Abstract

We study the Toulouse limit of the multi-channel Kondo model defined as the limit of maximal anisotropy which can be achieved without changing the infrared behaviour of the model. It is shown that when the number of channels exceeds 2, the interactions do not vanish and the Toulouse limit remains a non-trivial field theory. Considerable simplifications take place only for k = 2, where the Bethe ansatz reproduces the results by Emery and Kivelson.