Solution of the Multichannel Coqblin-Schrieffer Impurity Model and Application to Multi-Level systems

Abstract

A complete Bethe Ansatz solution of the SU(N)xSU(f) Coqblin Schrieffer model and a detailed analysis of some physical applications of the model are given. As in the usual multichannel Kondo model a variety of Fermi liquid and non-Fermi liquid (NFL) fixed points is found, whose nature depends on the impurity representation, $\mu$. For $\mu=f$ we find a Fermi liquid fixed point, with the impurity spin completely screened. For $f>\mu$ the impurity is overscreened and the model has NFL properties. The form the NFL behavior takes depends on the N and f: for $N\le f$ the specific heat and the susceptibility are dominated by the NFL contributions, for N>f the leading contributions are Fermi-liquid like and the NFL behavior can be seen only to subleading order, while for N=f the behavior is marginal. We also analyze the possibility of physical realizations. We show by a detailed renormalization group and 1/f analysis that the tunneling N-state problem can be mapped into the SU(N)xSU(f) exchange model, and discuss the subtle differences between the two models. As another physical realization we suggest a double quantum dot structure that can be described by means of an SU(3)xSU(2) model if the parameters of the dots are tuned appropriately.