Properties of magnetic impurities embedded into an anisotropic Heisenberg chain with spin gap

Abstract

We consider a U(1)-invariant model consisting of the integrable anisotropic easy-axis Heisenberg chain of arbitrary spin S embedding an impurity of spin S′. The host chain has a spin gap for all values of S. The ground state properties and the elementary excitations of the host are studied as a function of the anisotropy and the magnetic field. The impurity is located on a link of the chain and interacts only with both neighboring sites. The coupling of the impurity to the lattice can be tuned by the impurity rapidity p 0 (usually playing the role of the Kondo coupling). The impurity model is then integrable as a function of two continuous parameters (the anisotropy and the impurity rapidity) and two discrete variables (the spins S and S′). The Bethe ansatz equations are derived and used to obtain the magnetization of the impurity. The impurity magnetization is non-universal as a function of p 0. For small fields the impurity magnetization is determined by the spin gap and the van Hove singularity of the rapidity band. For an overcompensated impurity ( S′< S) at intermediate fields there is a crossover to non-Fermi-liquid behavior remnant from the suppressed quantum critical point.