Two Magnetic Impurities in a Spin Chain

TL;DR

This paper investigates the Kondo magnetic effect in an exactly solvable XXZ spin chain with boundary impurities, providing explicit formulas for thermodynamic properties and the Kondo temperature.

Contribution

It introduces an exactly solvable model of boundary impurities in an XXZ spin chain and derives explicit thermodynamic quantities using Bethe ansatz.

Findings

Finite size corrections to ground state energy are calculated.

Specific heat and susceptibility due to impurities are derived.

Kondo temperature is explicitly given.

Abstract

In this letter, the Kondo magnetic effect is studied for the $XXZ$ spin chain where the impurities are coupled to the edges of the system. The Hamiltonian of our model can be constructed from the transfer matrix. It is exactly solvable and the exchange constants between the bulk and the boundary impurities are arbitrary. The finite size corrections to the ground state energy are obtained for the magnetic impurities and the boundary condition. The specific heat and the susceptibility contributed by the impurities are derived and the Kondo temperature is given explicitly by the use of the Luttinger-Fermi liquid picture and the Bethe ansatz method.