FORMATION OF THE HALDANE PHASE BY SOLITON-PAIR DISSOCIATION - RESULTS FROM A CLUSTER APPROXIMATION

We study the structure and properties of the ground state of an antiferromagnetic S = 1 spin chain with single-ion anisotropy energy d and exchange anisotropy energy epsilon. We apply the nonlocal unitary transformation of Kennedy and Tasaki to take into account the essential correlations and restrict our study to the subspace of spin-zero defects (solitons). We investigate the quantum phase transitions in the (epsilon,d) plane in a cluster approximation which takes into account correlations between spins at 3 neighboring sites in the unitarily transformed representation. We obtain quantitative results for the phase diagram, for the values of the hidden order parameter, and for amplitudes that describe the transition from the Neel to the Haldane phase in terms of the dissociation of soliton pairs.