Exact solution of the open Heisenberg chain with two impurities

TL;DR

This paper presents an exactly solvable integrable model of a spin-1/2 Heisenberg chain with two impurities, analyzing impurity screening, residual entropy, and Kondo temperature using Bethe ansatz methods.

Contribution

It introduces a new exactly solvable model of the Heisenberg chain with impurities, providing explicit solutions and physical insights into impurity screening and thermodynamics.

Findings

Impurity spins can only be screened with antiferromagnetic coupling.

Residual entropy and Kondo temperature are explicitly derived.

Model is exactly solvable for arbitrary impurity parameters.

Abstract

We propose an integrable model of the spin-1/2 Heisenberg chain coupled to two impurity moments. With the open boundary conditions at the impurity sites, the model can be exactly solved for arbitrary impurity spin and arbitrary exchange constants between the bulk and the impurities. The absence of redundant terms in the hamiltonian makes the model very reasonable. The hamiltonian is diagonalized via algebraic Bethe ansatz. It is found that the impurity spins can only be screened (partially for $S>1/2$) for antiferromagnetic coupling between the impurity and the bulk. Otherwise the impurity spins can not be screened. The residual entropy of the ground state and the Kondo temperature are also derived explicitly based on the thermodynamic Bethe ansatz and the local Fermi liquid theory.