Kondo Effect in a Luttinger Liquid: Exact Results from Conformal Field Theory

TL;DR

This paper provides exact low-temperature thermodynamic results for a magnetic impurity in a one-dimensional interacting electron system, revealing two critical behaviors and linking back scattering suppression to the two-channel Kondo effect.

Contribution

It applies boundary conformal field theory to classify critical behaviors of a Kondo impurity in a Luttinger liquid, identifying two distinct types and their relation to known phenomena.

Findings

Two types of critical behavior identified: local Fermi liquid and anomalous response.

Suppression of back scattering yields properties similar to the two-channel Kondo effect.

Exact results for thermodynamics at low temperatures in a 1D interacting system.

Abstract

We report on exact results for the low-temperature thermodynamics of a spin-$\frac{1}{2}$ magnetic impurity coupled to a one-dimensional interacting electron system. By using boundary conformal field theory, we show that there are only two types of critical behaviors consistent with the symmetries of the problem: {\em either} a local Fermi liquid, {\em or} a theory with an anomalous response identical to that recently proposed by Furusaki and Nagaosa. Suppression of back scattering off the impurity leads to the same critical properties as for the two-channel Kondo effect.