Bosonization in the two-channel Kondo model

TL;DR

This paper demonstrates two equivalent bosonization representations of the anisotropic two-channel Kondo model, including an extension of the Emery-Kivelson approach and a novel ($\sigma$,$ au$) description, establishing their formal equivalence.

Contribution

It introduces a new ($\sigma$,$ au$) bosonization representation and proves its equivalence to the traditional two-channel Kondo model, extending the Emery-Kivelson approach.

Findings

Two equivalent bosonization representations of the two-channel Kondo model.

Extension of the Emery-Kivelson approach to include a resonant level model.

Formal proof of the equivalence between the ($\sigma$,$ au$) model and the two-channel Kondo model.

Abstract

The bosonization of the $S=1/2$ anisotropic two-channel Kondo model is shown to yield two equivalent representations of the original problem. In a straight forward extension of the Emery-Kivelson approach, the interacting resonant level model previously derived by the Anderson-Yuval technique is obtained. In addition, however, a ``($\sigma$,$\tau$)'' description is also found. The strong coupling fixed point of the ($\sigma$,$\tau$) model was originally postulated to be related to the intermediate coupling fixed point of the two-channel Kondo model. The equivalence of the $\sigma$,$\tau$ model to the two-channel Kondo model is formally established. A summary of what one may learn from a simple study of these different representations is also given.