Spin-one Kitaev-Heisenberg model on a two-dimensional honeycomb lattice

We study the Kitaev-Heisenberg model with a spin-1 local degree of freedom on a two-dimensional honeycomb lattice numerically by density matrix renormalization group method. We obtain the phase diagram with two spin liquid phases and four symmetry broken phases. We identify that the spin liquid is gapless and has short-ranged spin-spin correlations within the whole phase. Comparing to its spin-1/2 counterpart, the spin-1 spin liquid has more gapless modes.