Kondo effect in crossed Luttinger liquids

TL;DR

This paper investigates the Kondo effect in crossed Luttinger liquids using Boundary Conformal Field Theory, revealing two critical behaviors and linking to multi-channel Kondo models and two-band Hubbard systems.

Contribution

It introduces a theoretical analysis of the Kondo effect in crossed Luttinger liquids, identifying new critical behaviors and connections to multi-channel Kondo theories.

Findings

Identification of two types of critical behavior in crossed Luttinger liquids.

Prediction of a nonuniversal Wilson ratio at the two-channel Kondo fixed point.

Linking the suppression of backscattering to a four-channel Kondo model.

Abstract

We study the Kondo effect in two crossed Luttinger liquids, 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 new theory with an anomalous response 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, and we make links 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.