A striped supersolid phase and the search for deconfined quantum   criticality in hard-core bosons on the triangular lattice
  Using large-scale quantum Monte Carlo simulations we study bosons hopping on a triangular lattice with nearest (V) and next-nearest (V') neighbor repulsive interactions. In the limit where V=0 but V' is large, we find an example of an unusual period-three striped supersolid state that is stable at 1/2-filling. We discuss the relationship of this state to others on the rich ground-state phase diagram, which include a previously-discovered nearest-neighbor supersolid, a uniform superfluid, as well as several Mott insulating phases. We study several superfluid- and supersolid-to-Mott phase transitions, including one proposed by a recent phenomenological dual vortex field theory as a candidate for an exotic deconfined quantum critical point. We find no examples of unconventional quantum criticality among any of the interesting phase transitions in the model. 
R. G. Melko, A. Del Maestro and A. A. Burkov