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We investigate the zero-temperature phase diagram of the one-dimensional S=1Heisenberg antiferromagnet with single-ion anisotropy. By employing high-orderseries expansions and quantum Monte Carlo simulations we obtain accurateestimates for the critical points separating different phases in the quantumphase diagram. Additionally, excitation spectra and gaps are obtained.

Quantum Phase Diagram and Excitations for the One-Dimensional S=1 Heisenberg Antiferromagnet with Single-Ion Anisotropy