Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid

TL;DR

This paper introduces exactly solvable models combining Calogero-Sutherland and Kondo interactions to study impurity screening in Luttinger liquids, revealing fractionalization and conformal field theory connections.

Contribution

It develops new exactly solvable models for Kondo impurities in Luttinger liquids with explicit ground state wave functions and conformal field theory insights.

Findings

Ground states have Jastrow product forms with particle-statistics-dependent powers

Wave functions can be expressed as conformal field theory correlators

Particles fractionalize to fully screen the Kondo impurity

Abstract

We propose a series of models with inverse-square interactions, for which the ground states have an exact closed form, that describe one localized spin-$1/2$ Kondo impurity coupled to Luttinger liquids of itinerant bosons or fermions in the continuum or on a lattice. The model Hamiltonians contain two parts: a two-component Calogero-Sutherland model with open boundary condition in the continuum or a long-range $t \textendash J$-type model on the lattice, and long-range Kondo couplings between the impurity and the particles. The wave functions of the ground states in a certain basis have Jastrow product forms with powers depending on the particle statistics. It is shown that the wave functions can be expressed as chiral correlators of certain conformal field theories, which reveals that the particles are fractionalized to fully screen the Kondo impurity. This insight would be very useful in future studies on the very difficult problem of Kondo physics with interacting baths.