  We explore the phase diagram of the strongly correlated Hubbard model with
intrinsic spin orbit coupling on the honeycomb lattice. We obtain the low
energy effective model describing the spin degree of freedom. We study the
resulting model within the Schwinger boson and Schwinger fermion approaches.
The Schwinger boson approach gives the boundary between the spin liquid phase
and the magnetically ordered phases, Neel order and incommensurate Neel order.
We find that increasing the strength of the spin orbit coupling, narrows the
width of the spin liquid region. The Schwinger fermion approach sheds further
light on the nature of the spin liquid phase. We obtain three different
candidates for the spin liquid phase within the mean field approximation which
are gapless spin liquid, topological Mott insulator, and the chiral spin liquid
phases. We argue that the gauge fluctuations and the instanton effect may
suppress the first two spin liquids, while the chiral spin liquid is stable
against gauge fluctuations due to its nontrivial topology.
