Phase diagrams, critical, and multicritical behavior of hard-core Bose-Hubbard models

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.