The Bose-Hubbard model on a triangular lattice with diamond   ring-exchange
  Ring-exchange interactions have been proposed as a possible mechanism for a Bose-liquid phase at zero temperature, a phase that is compressible with no superfluidity. Using the Stochastic Green Function algorithm (SGF), we study the effect of these interactions for bosons on a two-dimensional triangular lattice. We show that the supersolid phase, that is known to exist in the ground state for a wide range of densities, is rapidly destroyed as the ring-exchange interactions are turned on. We establish the ground-state phase diagram of the system, which is characterized by the absence of the expected Bose-liquid phase. 
V.G. Rousseau, K. Hettiarachchilage, K.-M. Tam, M. Jarrell, J. Moreno
cond-mat.str-el