An Exactly Solvable Kondo Problem for Interacting One-Dimensional Fermions

TL;DR

This paper provides an exact solution to a one-dimensional Kondo problem for interacting fermions, confirming a conjecture about ferromagnetic screening and deriving key thermodynamic properties.

Contribution

It introduces an exactly solvable model for the 1D Kondo problem and clarifies conditions for ferromagnetic screening using Bethe ansatz.

Findings

Ferromagnetic Kondo screening occurs in one case, confirming the Furusaki-Nagaosa conjecture.

Surface energy, specific heat, and susceptibility are explicitly derived.

The Kondo temperature is calculated from the thermodynamic properties.

Abstract

The single impurity Kondo problem in the one-dimensional $\delta$-potential Fermi gas is exactly solved for two sets of special coupling constants via Bethe ansatz. It is found that ferromagnetic Kondo screening does occur in one case which confirms the Furusaki-Nagaosa conjecture while in the other case it does not, which we explain in a simple physical picture. The surface energy, the low temperature specific heat and the Pauli susceptibility induced by the impurity and thereby the Kondo temperature are derived explicitly.