Bosonization solution of the Kondo lattice in a Luttinger liquid

TL;DR

This paper uses bosonization to solve the Kondo lattice problem in a one-dimensional Luttinger liquid, revealing how electron interactions influence Kondo and RKKY physics.

Contribution

It identifies special interaction values allowing exact refermionization, providing new solvable limits for impurity correlations in the Kondo lattice.

Findings

Exact solutions at special interaction points

Interaction sign determines Kondo or RKKY dominance

Impurity correlations linked to extended or local order

Abstract

We address the physics of a regular arrangement of independent magnetic impurities embedded in a band of interacting electrons. We focus on the one-dimensional case that can be studied using bosonization and in which the electron bulk is described by a Luttinger liquid. The impurity spins interact with the electrons via magnetic exchange that introduces the possibility of Kondo and RKKY physics. We find that for two special values of the interactions, the model can be refermionized as a non-interacting electron band hybridized with a regular array of resonant levels. These solvable limits provide access to impurity correlators that correspond to either extended algebraic order or local screening. A physical picture emerges of how the interelectron interactions can stabilize either Kondo or RKKY physics depending on the sign of the interaction.