Enhanced Local Moment Formation in a Chiral Luttinger Liquid

TL;DR

This paper investigates how correlations in a chiral Luttinger liquid stabilize local magnetic moments and lead to Kondo physics, revealing new insights into impurity behavior in strongly interacting one-dimensional systems.

Contribution

It derives a stability condition for local moments in a chiral Luttinger liquid and maps the problem to a Kondo model with anisotropic exchange interactions.

Findings

Correlations stabilize local moments in the Luttinger liquid.

The impurity problem maps onto a Kondo model with anisotropic exchange.

Ground-state properties mirror those of the Kondo effect in a Luttinger liquid.

Abstract

We derive here a stability condition for a local moment in the presence of an interacting sea of conduction electrons. The conduction electrons are modeled as a Luttinger liquid in which chirality and spin are coupled. We show that an Anderson-U defect in such an interacting system can be transformed onto a nearly-Fermi liquid problem. We find that correlations among the conduction electrons stabilize the local moment phase. A Schrieffer-Wolff transformation is then performed which results in an anisotropic exchange interaction indicative of the Kondo effect in a Luttinger liquid. The ground-state properties of this model are then equivalent to those of the Kondo model in a Luttinger liquid.