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Journal of Physics A Mathematical and General

Exact solution of generalized t-J models in one dimension

R. Z. Bariev

Published May 21, 1994• 20 citations
Publisher

Abstract

A relation between the anisotropic t-J model and a generalized six-vertex model has been established. On the basis of this relation, we obtain the exact Bethe ansatz solution for the ground state energy of anisotropic t-J model for arbitrary spin and special values of coupling parameters. We consider also the anisotropic generalization of t-J model with localons.

DOI
10.1088/0305-4470/27/10/013

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A relation between the anisotropic t-J model and a generalized six-vertex model has been established. On the basis of this relation, we obtain the exact Bethe ansatz solution for the ground state energy of anisotropic t-J model for arbitrary spin and special values of coupling parameters. We consider also the anisotropic generalization of t-J model with localons.
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A multicomponent anisotropic $t\ensuremath{-}J$ model with a hard-core potential is formulated and solved by the Bethe ansatz method in one dimension for an arbitrary core radius $(\ensuremath{\Delta}+1)/2.$ The ground-state Bethe equations are analyzed and solved numerically for an arbitrary band filling, several values of color components, and the coupling constants. The ground-state energy, the Fermi velocity, and the critical exponents of the correlation functions have been calculated numerically for an arbitrary density of electrons. We discuss the effect of the hard-core potential. The Fermi velocity has a maximum as a function of band filling, vanishing for the empty and full bands. In comparison to the traditional anisotropic $t\ensuremath{-}J$ model in which $\ensuremath{\Delta}=0,$ the Fermi velocity is strongly enhanced in general. In the high-density limit, there is no dynamics of charges, the model exhibits a metal-insulator phase transition, and reduces to an antiferromagnetic spin chain with a new spacing parameter $\ensuremath{\Delta}+1.$
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-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 $t\ensuremath{-}J$ 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.