Perturbative renormalization of multi-channel Kondo-type models

TL;DR

This paper extends the poor man's scaling method to third order using perturbation theory for a generalized SU(n)×SU(m) Kondo model, revealing both Fermi-liquid and non-Fermi-liquid fixed points and their stability.

Contribution

It introduces a higher-order renormalization approach for a generalized Kondo model with SU(n)×SU(m) symmetry, analyzing fixed points and stability.

Findings

The model exhibits both Fermi-liquid and non-Fermi-liquid fixed points.

The non-Fermi-liquid fixed point is unstable when n=m=2.

Potential relevance to phase IV in Ce_xLa_{1-x}B_6 is discussed.

Abstract

The poor man's scaling is extended to higher order by the use of the open-shell Rayleigh-Schroedinger perturbation theory. A generalized Kondo-type model with the SU(n) times SU(m) symmetry is proposed and renormalized to the third order. It is shown that the model has both local Fermi-liquid and non-Fermi-liquid fixed points, and that the latter becomes unstable in the special case of n=m=2. Possible relevance of the model to the newly found phase IV in Ce_{x}La_{1-x}B_6 is discussed.