Haldane Gap and the Spin 1 Antiferromagnetic Integrable Model

Abstract

We have studied the Spin 1 antiferromagnetic chain with both bilinear and biquadratic exchange interactions. The spin correlations have been calculated by means of the transfer matrix method based on the Trotter formula. The mass gap (m(0)) at the ground state has been investigated as a function of the ratio λ between bilinear and biquadratic interactions. The result suggests that the gapless ground state persists in a finite range of λ, i.e., λ_c<λ<λ₁, with λ_c=0.5 and λ₁>1 which is consistent with the exact solution at the completely integrable point (λ=1). The calculated mass gap (m(0)) has been fitted to a Kosterlitz-Thouless (KT)-type for λ<λ_c (m(0)=A exp [−B⁄(λ_c−λ)^σ]) producing the results σ=0.49±0.04 and λ_c=0.49±0.03.