We study the finite-temperature nature of a quantum phase transition between an Abelian and a non-Abelian topological phase in an exactly solvable model of the chiral spin liquid of Yao and Kivelson [Phys. Rev. Lett. 99, 247203 (2007)]. As it is exactly solvable, this model can serve as a testbed for developing better measures for describing topological quantum phase transitions. We use the global flux and entanglement entropy to characterize this phase transition, and we discuss to what extent the existence of a topologically ordered ground state with non-Abelian excitations is revealed at finite temperature.
We study
S=1 spin liquid states on the kagome lattice constructed by Gutzwiller-projected
px+ipy 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
Z2 Abelian spin liquid.