  We search for short-range Hamiltonians of finite spin-1 kagome systems,
maximizing the overlaps with lattice Moore-Read states. Our starting point is
an exact, long-range parent Hamiltonian for such a state on a finite plane,
obtained from conformal field theory. A truncation procedure is applied to it,
which retains only short-range terms and makes it easy to define the
Hamiltonian on a torus. Finally, the remaining coefficients are optimized, to
yield maximized overlaps between exact diagonalization results and model ground
states. In the best cases, these overlaps exceed 0.9 and 0.8 for the three
lowest states of 12- and 18-site systems, respectively, suggesting that the
obtained Hamiltonians are good parent Hamiltonians for a non-Abelian
topological order.
