Solution of the multichannel Coqblin-Schrieffer impurity model and application to multilevel systems

A complete Bethe ansatz solution of the $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}\times \mathrm{SU}\left(f\right)$ 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 μ. For $\mu =f,$ we find a Fermi-liquid fixed point, with the impurity spin completely screened. For $f>\mathrm{}\mu ,$ the impurity is overscreened and the model has NFL properties. The form the NFL behavior takes depends on the $N$ and $f:$ for $N<~f,$ 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; and 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 $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}\times \mathrm{SU}\left(f\right)$ 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 $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$ model if the parameters of the dots are tuned appropriately.