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

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.