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arXiv:cond-mat/9706228 · Physical review. B, Condensed matter

Exact solution of the biquadratic spin-1 t−J model in one dimension

Francisco Castilho Alcaraz, R. Z. Bariev

Published Oct 1, 1997• 3 citations
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Abstract

A generalization of the $t\ensuremath{-}J$ model with a nearest-neighbor hopping is formulated and solved exactly by the Bethe ansatz method. The model describes the dynamics of spin-$S$ fermions with isotropic or anisotropic interactions. In the case $S=1$ the magnetic interaction is biquadratic in the spin operators. In contrast to the $\mathrm{SU}(N)$ generalization of the $t\ensuremath{-}J$ model, studied previously in the literature, the present model possesses beyond a massless excitation also a massive one. The physical properties indicate the existence of Cooper-type pairs with finite binding energy.

DOI
10.1103/physrevb.56.7796

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A generalization of the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model with a nearest-neighbor hopping is formulated and solved exactly by the Bethe ansatz method. The model describes the dynamics of spin-SSS fermions with isotropic or anisotropic interactions. In the case S=1S=1S=1 the magnetic interaction is biquadratic in the spin operators. In contrast to the SU(N)\mathrm{SU}(N)SU(N) generalization of the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model, studied previously in the literature, the present model possesses beyond a massless excitation also a massive one. The physical properties indicate the existence of Cooper-type pairs with finite binding energy.
The one-dimensional anisotropic t - J model was exactly solved using the Bethe ansatz . We first discuss the effect of anisotropy on the ground-state properties. We find a continuous phase transition induced by a magnetic field. The low-lying (spin and charge) excitation spectrum is obtained for various fillings. According to the anisotropy, the model has massive or massless modes for spin excitations. At half-filling, the model reduces to the spin- antiferromagnetic XXZ -model. We calculate the correct excitation continuum whose lowest mode is lower than that obtained by des Cloizeaux and Gaudin. Charge excitations are massless for any value of the anisotropy.
An integrable spin-ladder model with nearest-neighbor exchanges and biquadratic interactions is proposed. With the Bethe ansatz solutions of the model Hamiltonian, it is found that there are three possible phases in the ground state, i.e., a rung-dimerized phase with a spin gap, and two massless phases. The possible fixed points of the system and the quantum critical behavior at the critical point J=J+c{J=J}_{+}^{c}J=J+c​ are discussed.