Quantum Phase Diagram and Excitations for the One-Dimensional S=1   Heisenberg Antiferromagnet with Single-Ion Anisotropy
  We investigate the zero-temperature phase diagram of the one-dimensional S=1 Heisenberg antiferromagnet with single-ion anisotropy. By employing high-order series expansions and quantum Monte Carlo simulations we obtain accurate estimates for the critical points separating different phases in the quantum phase diagram. Additionally, excitation spectra and gaps are obtained. 
A. Fabricio Albuquerque, Chris J. Hamer, and Jaan Oitmaa