  We determine the zero-temperature phase diagram of the hard-core Bose-Hubbard
model on a square lattice by mean-field theory supplemented by a linear
spin-wave analysis. Due to the interplay between nearest and next-nearest
neighbor interaction and cubic anisotropy several supersolid phases with
checkerboard, stripe domain or intermediate symmetry are stabilized. The phase
diagrams show three different topologies depending on the relative strength of
nearest and next-nearest neighbor interaction. We also find a rich variety of
new quantum critical behavior and multicritical points and discuss the
corresponding effective actions and universality classes.
