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Gutzwiller study of extended Hubbard models with fixed boson densities

We studied all possible ground states, including supersolid (SS) phases and phase separations of hard-core- and soft-core-extended Bose--Hubbard models with fixed boson densities by using the Gutzwiller variational wave function and the linear programming method. We found that the phase diagram of the soft-core model depends strongly on its transfer integral. Furthermore, for a large transfer integral, we showed that an SS phase can be the ground state even below or at half filling against the phase separation. We also found that the density difference between nearest-neighbor sites, which indicates the density order of the SS phase, depends strongly on the boson density and transfer integral.