Spin Liquid Phases for Spin-1 Systems on the Triangular Lattice

Motivated by recent experiments on material Ba3NiSb2O9, we propose two novel spin liquid phases (A and B) for spin-1 systems on a triangular lattice. At the mean field level, both spin liquid phases have gapless fermionic spinon excitations with quadratic band touching; thus, in both phases the spin susceptibility and gamma = C-nu/T saturate to a constant at zero temperature, which are consistent with the experimental results on Ba3NiSb2O9. On the lattice scale, these spin liquid phases have Sp(4) similar to SO(5) gauge fluctuation, while in the long wavelength limit this Sp(4) gauge symmetry is broken down to U(1) x Z(2) in the type A spin liquid phase, and broken down to Z(4) in the type B phase. We also demonstrate that the A phase is the parent state of the ferroquadrupole state, nematic state, and the noncollinear spin density wave state.