Lattice fermion models with supersymmetry

We investigate a family of lattice models with manifest N = 2 supersymmetry. The models describe fermions on a ID lattice, subject to the constraint that no more than k consecutive lattice sites may be occupied. We discuss the special properties arising from the supersymmetry, and present Bethe ansatz solutions of the simplest models. We display the connections of the k = 1 model with the spin-1/2 antiferromagnetic XXZ chain at Delta = -1/2, and the k = 2 model 2 with both the su(2/1)-symmetric U model in the ferromagnetic regime and the integrable spin- 1 XXZ chain at Delta = - 1/root2. We argue that these models include critical points described by the superconformal minimal models.