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 ${\mathit{tsum}}_{\mathit{i}=1\mathrm{}}^{\mathit{N}}$ ${\mathbf{S}}_{\mathit{i}}$⋅${\mathbf{S}}_{\mathit{i}+1\mathrm{}}$+D tsum(${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ ${)}^2$] 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 D≠0, the elementary excitations in the subspace of ${\mathit{S}}^{\mathit{z}}$=±1 and in the subspace of ${\mathit{S}}^{\mathit{z}}$=0 are different. The ${\mathit{S}}^{\mathit{z}}$=±1 branch is lower than the ${\mathit{S}}^{\mathit{z}}$=0 branch near Q=π; however, it becomes slightly higher in other regions. The crossing of levels occurs at Q≃±0.7π. We find that the low-lying excited state has a weight of more than 90% in the dynamical structure factor, except for Q≃0. Our results explain recent experimental results on Ni(${\mathrm{C}}_2$ ${\mathrm{H}}_8$ ${\mathrm{N}}_2$ ${)}_2$ ${\mathrm{NO}}_2$ ${\mathrm{ClO}}_4$.