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

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 po) 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 c --> 0 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, H-c,(c, po) and H-s,(c, po), at which the susceptibility diverges. H-c,tends to zero as c --> 0 giving rise to a crossover from non-Fermi-liquid behaviour for H < H,to Fermi-liquid-like behaviour for H < II,. 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.