A multi-channel fixed point for a Kondo spin coupled to a junction of Luttinger liquids

TL;DR

This paper investigates the Kondo effect in a junction of Luttinger liquids, revealing different fixed points depending on the junction's scattering matrix, with implications for spin interactions and temperature dependence.

Contribution

It introduces a renormalization group analysis of a Kondo impurity coupled to Luttinger liquid junctions, identifying conditions for multi-channel and strong coupling fixed points.

Findings

Multi-channel fixed point for repulsive interactions with decoupled S-matrix.

Flow to strong coupling fixed point with Griffiths S-matrix.

Characteristic temperature dependence of spin-flip scattering.

Abstract

We study a system of an impurity spin coupled to a junction of several Tomonaga-Luttinger liquids using a renormalization group scheme. For the decoupled S-matrix at the junction, there is a range of Kondo couplings which flow to a multi-channel fixed point for repulsive inter-electron interactions; this is associated with a characteristic temperature dependence of the spin-flip scatterings. If the junction is governed by the Griffiths S-matrix, the Kondo couplings flow to a strong coupling fixed point where all the wires are decoupled.