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Journal of the Physical Society of Japan

A New Phase of theS=1 Bilinear-Biquadratic Chain: -a Trimerized State-

K. Nomura, Satoshi Takada

Published Feb 15, 1991• 28 citations
Publisher

Abstract

We investigate the S =1 bilinear-biquadratic model. In some region, the trimerized variational state is a good candidate for the ground state. This explains why the Sutherland model ( J 1 >0 and J 2 / J 1 =-1) has soft modes at q =0, ±2π/3. Moreover, the full phase diagram of this model is discussed. It is found that at the pure biquadratic ferromagnetic point, the ground state is extremely degenerate.

DOI
10.1143/jpsj.60.389

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We study numerically the elementary excitation spectrum of the most general isotropic spin-1 chain with bilinear-biquadratic nearest-neighbor coupling. Using finite-size scaling, a massless phase with a period tripling in the ground state is found to exist in an extended region around the Lai-Sutherland point. The location of the transition from the known valence-bond-like phase to the trimerized phase cannot, however, be given precisely. We also present results on the ground-state two-point correlation function.
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The possible ground states and the phase transitions of a spin-1 chain with bilinear-biquadratic exchange are studied numerically. In order to see better the real asymptotic behavior of the infinite system and to determine the necessary degeneracies, a twisted boundary condition is used that reduces the finite-size effects. This calculation confirms that a second-order Ising-type phase transition occurs at the Takhtajan-Babujian point from the dimerized phase to the singlet Haldane phase. The transition at the Lai-Sutherland point, to a massless phase with three soft modes, is found to be of Kosterlitz-Thouless type.