Non-Abelian chiral spin liquid on a spin-1 kagome lattice: Truncation of an exact Hamiltonian and numerical optimization

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 such a state on plane, obtained from conformal field theory. A truncation procedure applied to it, which retains only terms and makes it easy define torus. Finally, remaining coefficients are optimized, yield maximized between exact diagonalization results model ground In best cases, these exceed 0.9 0.8 three lowest states 12- 18-site respectively, suggesting that good non-Abelian topological order.