  Motivated by the recent experimental realization of the Haldane model by
ultracold fermions in an optical lattice, we investigate phase diagrams of the
hard-core Bose-Hubbard model on a honeycomb lattice. This model is closely
related with a spin-1/2 antiferromagnetic (AF) quantum spin model.
Nearest-neighbor (NN) hopping amplitude is positive and it prefers an AF
configurations of phases of Bose-Einstein condensates. On the other hand, an
amplitude of the next-NN hopping depends on an angle variable as in the Haldane
model. Phase diagrams are obtained by means of an extended path-integral
Monte-Carlo simulations. Besides the AF state, a 120$^o$-order state, there
appear other phases including a Bose metal in which no long-range orders exist.
