Critical Properties ofS=1 XXZ Chain

The S x - S x correlation function of S =1 XXZ chain is calculated at low temperatures by means of the transfer matrix with use of the Trotter formula. Critical properties of the correlation function, such as critical indices γ, η and ν and the mass identified by the inverse correlation length at T =0, are obtained. We conclude that a groundstate with an excitation gap appears for the anisotropy parameter Δ<Δ 1 ≃ -0.3 including the isotropic antiferromagnetic point (Δ=-1). We have obtained η≃1/4 at Δ=Δ 1 in accord with the theoretical prediction by Haldane and den Nijs. Our result, however, shows the monotonic increase of the excitation gap with decreasing Δ for Δ<Δ 1 contrary to Haldane's prediction.