Magnetic Impurity in a Luttinger Liquid: A Conformal Field Theory Approach

TL;DR

This paper uses boundary conformal field theory to analyze the low-temperature behavior of a magnetic impurity in a Luttinger liquid, revealing critical scaling, fixed points, and possible Fermi liquid or non-Fermi liquid states.

Contribution

It applies boundary conformal field theory to impurity problems in Luttinger liquids, identifying new fixed points and scaling behaviors for different scattering regimes.

Findings

Forward scattering yields Kondo-like critical scaling with a novel Wilson ratio.

Backward scattering destabilizes the critical behavior, leading to a new fixed point.

Equal forward and backward scattering can result in either a Fermi liquid or a critical non-Fermi liquid state.

Abstract

We study the low-temperature properties of a spin-\onehalf\ magnetic impurity coupled to a one-dimensional interacting electron system. Using the newly developed formalism by Affleck and Ludwig, with a scale invariant boundary condition replacing the impurity, we exploit boundary conformal field theory to deduce the impurity thermal and magnetic response. In the case of only forward electron scattering off the impurity, we predict the same critical scaling as for the two-channel Kondo effect for non-interacting electrons, but with a novel Wilson ratio. Backward electron scattering off the impurity destabilizes this behavior and drives the system to a new fixed point. In the case of equal amplitudes for forward- and backward scattering {\em (Kondo interaction)}, we show that there are only two types of scaling behaviors consistent with the symmetries of the problem: {\em either} a local Fermi liquid {\em or} a critical theory with an anomalous specific heat. The latter case agrees with a recent ``poor-man-scaling'' result proposed by Furusaki and Nagaosa.