  We construct and study a class of N particle supersymmetric Hamiltonians with
nearest and next-nearest neighbor inverse-square interaction in one dimension.
We show that inhomogeneous XY models in an external non-uniform magnetic field
can be obtained from these super-Hamiltonians in a particular limit decoupling
the fermionic degrees of freedom from the kinematic ones. We further consider a
suitable deformation of these super-models such that inhomogeneous XXZ
Hamiltonians in an external non-uniform magnetic field are obtained in the same
limit. We show that this deformed Hamiltonian with rational potential is, (i)
mapped to a set of free super-oscillators through a similarity transformation
and (ii) supersymmetric in terms of a new, non-standard realization of the
supercharge. We construct many exact eigenstates of this Hamiltonian and
discuss about the applicability of this technique to other models.
