  In this paper, we study phase diagrams of dipolar hard-core boson gases on
the honeycomb lattice. The system is described by the Haldane-Bose-Hubbard
model with complex hopping amplitudes and the nearest neighbor repulsion. By
using the slave-particle representation of the hard-core bosons and also the
path-integral quantum Monte-Carlo simulations, we investigate the system and to
show that the systems have a rich phase diagram. There are Mott, superfluid,
chiral superfluid, and sublattice chiral superfluid phases as well as the
density-wave phase. We also found that there exists a coexisting phase of
superfluid and chiral superfluid. Critical behaviors of the phase transitions
are also clarified.
