The Heisenberg chain with impurities: crossover from Fermi-liquid to non-Fermi-liquid behaviour

Abstract

We consider an integrable SU(2)-invariant model consisting of a Heisenberg chain of spins S (the Takhtajan-Babujian model) interacting with a finite concentration c of impurity spins S´. The thermodynamic Bethe-ansatz equations are stated for this model. The ground-state equations are analysed as a function of c, the magnetic field and the coupling parameter (impurity rapidity p0) of the impurities to the lattice. In zero field the ground state is a singlet for finite c, but becomes non-Fermi-liquid-like as c0 for S´<S. Two rapidity bands play a role at T = 0 corresponding to strings of length 2S and 2S´, respectively. The van Hove singularities of the empty bands define two critical fields, Hc(c,p0) and Hs(c,p0), at which the susceptibility diverges. Hc tends to zero as c0 giving rise to a crossover from non-Fermi-liquid behaviour for H>Hc to Fermi-liquid-like behaviour for H<Hc. The spectrum of elementary excitations and the finite-size corrections to the ground-state energy are calculated, and used to discuss the asymptotic behaviour of spin-spin correlation functions for long times and large distances.