Non-Abelian chiral spin liquid in the frustrated spin-1 quantum antiferromagnet on the square lattice*

We investigate the ground state properties of the spin-1 antiferromagnetic Heisenberg J1-J2 model supplemented by time-reversal symmetry breaking chiral interaction on the square lattice using density-matrix renormalization group. Based on studies of numerous long cylinders with circumferences of up to 10 lattice spacings, we obtain strong evidence for a novel quantum spin liquid state in the ground state phase diagram. Remarkably, we find that this spin liquid is consistent with the non-Abelian Moore-Read chiral spin liquid, which is evidenced by both entanglement spectra and related flux threading experiments. Our results provide a concrete example of realizing the non-Abelian spin liquid in a general higher spin system, which is beyond previous attempts in spin-1/2 systems.