Elementary excitations of an anisotropic spin-1 chain

The neutron-scattering intensity and energy eigenvalues of the elementary excitations of the S=1 antiferromagnetic Heisenberg chain with single-ion anisotropy scrH=J tsum₈=₁^N S₈S₈+₁+D tsum (S₈^z) ^2 are calculated with a numerical diagonalization method and a projector Monte Carlo method. We set D/J=0. 2, 0. 0, -0. 2 and N=14, 16, 18, 32. For D0, the elementary excitations in the subspace of S^z=1 and in the subspace of S^z=0 are different. The S^z=1 branch is lower than the S^z=0 branch near Q=; however, it becomes slightly higher in other regions. The crossing of levels occurs at Q0. 7. We find that the low-lying excited state has a weight of more than 90% in the dynamical structure factor, except for Q0. Our results explain recent experimental results on Ni (C₂H₈N₂) ₂NO₂ClO₄.