Bosonization in 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 ``($σ$,$τ$)'' description is also found. The strong coupling fixed point of the ($σ$,$τ$) model was originally postulated to be related to the intermediate coupling fixed point of the two-channel Kondo model. The equivalence of the $σ$,$τ$ 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.