Critical Properties of S=1 XXZ Chain

Abstract

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<Δ₁\simeq−0.3 including the isotropic antiferromagnetic point (Δ=−1). We have obtained η\simeq1⁄4 at Δ=Δ₁ 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<Δ₁ contrary to Haldane’s prediction.