  We show the chiral d-wave RVB state on honeycomb lattice stands as a natural
generalization of the staggered flux phase on square lattice. Although the
state is generated from a time reversal symmetry broken mean field ansatz, it
actually represents a fully symmetric spin liquid state with a positive
definite wave function in the sense of Marshall sign rule for unfrustrated
antiferromagnets. The evolution of the state with the parameter $\Delta/\chi$
follows exactly the same manner as that of the staggered flux phase on square
lattice. The critical pairing strength corresponding to the $\pi$-flux phase is
found to be $\Delta/\chi=\sqrt{2}$. As a result of the geometric frustration
between neighboring plaquette on honeycomb lattice, a direct generalization of
the U(1) staggered flux pattern on square lattice to honeycomb lattice is
impossible. Replacing it is the chiral d-wave state with $Z_{2}$ gauge
structure. However, this $Z_{2}$ gauge structure is found to be ineffective
after Gutzwiller projection and the system does not support topological
degeneracy. The chiral d-wave RVB state is also found to be a rather good
variational state for the Heisenberg model on honeycomb lattice. The spin
correlation of the chiral d-wave state is found to be greatly enhanced as
compared to the mean field prediction.
