Finite-size-scaling study of the spin-1 Heisenberg-Ising chain with uniaxial anisotropy

Finite-cell calculations (up to $N=12$ spins) have been performed on the spin-1 Heisenberg-Ising chain with an uniaxial anisotropy, H=Σi^[SᵢˣSᵢ₊₁ˣ+SᵢʸSᵢ₊₁ʸ+λSᵢᶻSᵢ₊₁ᶻ+D(Sᵢᶻ)²]. From a scaling analysis of the gap between the ground state and the first excited state, a phase diagram has been drawn in the (λ,D) plane and the transition lines between the "ferromagnetic," X-Y," "singlet-ground-state," and "antiferromagnetic" phases have been estimated for the infinite-N system. One of the most important results is that a singlet-ground-state phase with a nonzero gap exists in an extended range of λ and D values including the Heisenberg point λ=1, $D=0$, in contrast with the spin-1/2 case. Moreover, for λ1, the gap decreases with increasing positive anisotropy D, goes through a minimum, estimated to be zero, and then increases with D.