Kondo effect in crossed Luttinger liquids

We present results for the Kondo effect in two crossed Luttinger liquids by using boundary conformal field theory. We predict two types of critical behaviors: either a two-channel Kondo fixed point with a nonuniversal Wilson ratio or a theory with an anomalous reponse that is identical to that found by Furusaki and Nagaosa for the Kondo effect in a single Luttinger liquid. Moreover, we discuss the relevance of perturbations like channel anisotropy in restoring a Fermi-liquid-like Kondo fixed point, and compare our results with the Kondo effect in a two-band Hubbard system modeled by a channel-dependent Luttinger Hamiltonian. The suppression of backscattering off the impurity produces a model similar to the four-channel Kondo theory. Consequences are discussed.