  We introduce a family of strongly-correlated spin wave functions on arbitrary
spin-1/2 and spin-1 lattices in one and two dimensions. These states are
lattice analogues of Moore-Read states of particles at filling fraction 1/q,
which are non-Abelian Fractional Quantum Hall states in 2D. One parameter
enables us to perform an interpolation between the continuum limit, where the
states become continuum Moore-Read states of bosons (odd q) and fermions (even
q), and the lattice limit. We show numerical evidence that the topological
entanglement entropy stays the same along the interpolation for some of the
states we introduce in 2D, which suggests that the topological properties of
the lattice states are the same as in the continuum, while the 1D states are
critical states. We then derive exact parent Hamiltonians for these states on
lattices of arbitrary size. By deforming these parent Hamiltonians, we
construct local Hamiltonians that stabilize some of the states we introduce in
1D and in 2D.
