  We study ground state properties and excitation spectra for hard-core Bosons
on square and triangular lattices, at half filling, using series expansion
methods. Nearest-neighbor repulsion between the Bosons leads to the development
of short-range density order at the antiferromagnetic wavevector, and
simultaneously a roton minima in the density excitation spectra. On the
square-lattice, the model maps on to the well studied XXZ model, and the roton
gap collapses to zero precisely at the Heisenberg symmetry point, leading to
the well known spectra for the Heisenberg antiferromagnet. On the
triangular-lattice, the collapse of the roton gap signals the onset of the
supersolid phase. Our results suggest that the transition from the superfluid
to the supersolid phase maybe weakly first order. We also find several features
in the density of states, including two-peaks and a sharp discontinuity, which
maybe observable in experimental realization of such systems.
