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Journal of Physics A Mathematical and General

One-dimensional Heisenberg XXZ magnetic chain with isolated impurities

Lin-Jie Jiang, Huan-Qiang Zhou

Published Jun 7, 1990• 7 citations
Publisher

Abstract

The one-dimensional (1D) Heisenberg XXZ magnetic chain with isolated impurities is presented as a new completely integrable system. This system includes the 1D Heisenberg XXZ model and the 1D Heisenberg XXX magnetic chain with isolated impurities as special limiting cases. The model Hamiltonian is diagonalised, and the algebraic Bethe ansatz equations are derived. This makes it possible to investigate the equilibrium thermodynamics of the system.

DOI
10.1088/0305-4470/23/11/031

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The one-dimensional (1D) Heisenberg XXZ magnetic chain with isolated impurities is presented as a new completely integrable system. This system includes the 1D Heisenberg XXZ model and the 1D Heisenberg XXX magnetic chain with isolated impurities as special limiting cases. The model Hamiltonian is diagonalised, and the algebraic Bethe ansatz equations are derived. This makes it possible to investigate the equilibrium thermodynamics of the system.
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We investigate Bethe Ansatz equations for the one-dimensional spin-12\frac{1}{2}21​ Heisenberg XXX chain with a special interest in a finite system. Solutions for the two-particle sector are obtained. The ground state in antiferromagnetic case has been analytically studied through the logarithmic form of Bethe Ansatz equations.
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>1/2S>1/2S>1/2) for antiferromagnetic coupling between the impurity and the bulk. Otherwise the impurity spins cannot be screened. The residual entropy of the ground state and the Kondo temperature are also derived explicitly based on the Bethe ansatz and the local Fermi-liquid theory.