Thermodynamics of a spin-S' impurity in a spin-S antiferromagnetic Heisenberg chain

Abstract

The numerical solution of the Bethe ansatz equations of an integrable SU(2)-invariant generalization of the spin-S antiferromagnetic Heisenberg chain (Takhtajian-Babujian model) with a spin-S' impurity in zero magnetic field is presented. The entropy, specific heat and susceptibility of an impurity of spin S' are obtained numerically as a function of the spin S of the chain. Three situations have to be distinguished: (i) if S'=S the impurity just corresponds to one more site in the chain; (ii) if S'>S the impurity spin is only partially compensated (undercompensated) at T=0, leaving an effective spin of (S'-S); (iii) if S'<S (overcompensated) the entropy has an essential singularity at T=h=0, giving rise to critical behaviour as h and T tend to zero. These properties are in close analogy with those of the n-channel Kondo problem. The thermodynamics of the two models is compared.