  In this paper, we investigate the topological Hubbard model on honeycomb
lattice. By considering the topological properties of the magnetic state, new
types of quantum states - A-type and B-type topological spin-density-waves
(A-TSDW and B-TSDW) are explored. The low energy physics is solely determined
by its Chern-Simons-Hopf gauge field theories with different K-matrices. In the
formulism of topological field theory, we found spin-charge separated
charge-flux binding effect for A-TSDW and spin-charge synchronized charge-flux
binding effect for B-TSDW. In addition, we studied the edge states and
quantized Hall effect in different TSDWs.
