U Q Osp(2, 2) Lattice Models

In this paper I construct lattice models with an underlying U q osp(2, 2) su-peralgebra symmetry. I find new solutions to the graded Yang-Baxter equation. These trigonometric R-matrices depend on three continuous parameters, the spectral parameter, the deformation parameter q and the U (1) parameter, b, of the superalgebra. It must be emphasized that the parameter q is generic and the parameter b does not correspond to the 'nilpotency' parameter of [15]. The rational limits are given; they also depend on the U (1) parameter and this dependence cannot be rescaled away. I give the Bethe ansatz solution of the lattice models built from some of these R-matrices, while for other matrices , due to the particular nature of the representation theory of osp(2, 2), I conjecture the result. The parameter b appears as a continuous generalized spin. Finally I briefly discuss the problem of finding the ground state of these models.