HALDANE GAPS IN A SPIN-1 HEISENBERG CHAIN WITH EASY-PLANE SINGLE-ION-ANISOTROPY

We study a Heisenberg antiferromagnetic chain of spin S = 1 with nearest-neighbor exchange interaction J and easy-plane single-ion anisotropy D. We follow the splitting of the Haldane gap into two components as a function of the anisotropy. Chains of length up to 16 sites are studied by a Lanczos method and longer chains up to 32 sites have been investigated by a quantum Monte Carlo simulation for D/J = 0.10, 0.15, 0.20, and 0.25. A careful finite-size scaling treatment of our data leads to values that are directly relevant to the interpretation of experiments on Ni(C2H8N2)2NO2ClO4 (NENP). We discuss the relationship between our results and the magnetic-susceptibility measurements as well as the inelastic-neutron-scattering data and on the Haldane conjecture. Values are proposed for the parameters D and J in the case of NENP.