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We discuss the appearance of supersolid phases for interacting hardcorebosons on the square lattice when, in addition to the standard nearest neighborhopping and repulsion, correlated or next-nearest neighbor hopping is present.Having in mind dimer-based quantum magnets in a field described by effectivebosonic models of this kind, we put special emphasis on a comparison betweenthe different cases of relative signs of the kinetic processes, whichcorrespond to unfrustrated or frustrated magnetic models. In the unfrustratedcase, we compare Quantum Monte Carlo simulations with a mean-field (classical)approach, which is shown to give qualitatively correct results. Using thisclassical approach for the frustrated case, we find that the phase diagram isgenerically richer than in the unfrustrated case. We also investigate in detailthe differences between standard next-nearest neighbour and correlated hoppingover the diagonal, with the conclusion that both cases are similar ifcheckerboard order is present at half-filling, while a supersolid phase can bestabilized without any adjacent solid phase only in the case of correlatedhopping.

Supersolid phases of hardcore bosons on the square lattice: Correlated hopping, next-nearest neighbor hopping and frustration