Non-Abelian S=1 chiral spin liquid on the kagome lattice

We study S = 1 spin liquid states on the kagome lattice constructed by Gutzwiller-projected p(x)+ip(y superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian )topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices S and T, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the SO(3)(1) (or, equivalently, SU(2)(2)) field-theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study, we observe a topological phase transition from the NACSL to the Z(2) Abelian spin liquid.