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We systematically study an extended Bose-Hubbard model with atom hopping andatom-pair hopping in the presence of a three-body constraint on the triangularlattice. By means of large-scale Quantum Monte Carlo simulations, theground-state phase diagram are studied. We find a continuous transition betweenthe atomic superfluid phase and the pair superfluid when the ratio of theatomic hopping and the atom-pair hopping is adapted. We then focus on theinterplay among the atom-pair hopping, the on-site repulsion and thenearest-neighbor repulsion. With on-site repulsion present, we observe firstorder transitions between the Mott Insulators and pair superfluid driven by thepair hopping. With the nearest-neighbor repulsion turning on, three typicalsolid phases with 2/3, 1 and 4/3-filling emerge at small atom-pair hoppingregion. A stable pair supersolid phase is found at small on-site repulsion.This is due to the three-body constraint and the pair hopping, whichessentially make the model a quasi hardcore boson system. Thus the pairsupersolid state emerges basing on the order-by-disorder mechanism, by whichhardcore bosons avoid classical frustration on the triangular lattice. Thetransition between the pair supersolid and the pair superfluid is first order,except for the particle-hole symmetric point. We compare the results with thoseobtained by means of mean-field analysis.

Pair supersolid of the extended Bose-Hubbard model with atom-pair hopping on the triangular Lattice