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=i^S₈^xS₈+₁^x+S₈^yS₈+₁^y+S₈^zS₈+₁^z+D ({S₈^z) }^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 (, 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 and D values including the Heisenberg point =1, D=0, in contrast with the spin-12 case. Moreover, for 1, the gap decreases with increasing positive anisotropy D, goes through a minimum, estimated to be zero, and then increases with D.