Abstract
We study the order of the zero temperature quantum phase transitions at density \ensuremath{\rho}=1 in the one-dimensional extended boson Hubbard model by examining the order parameter distribution and hysteresis effects. The phase diagram of the model at \ensuremath{\rho}=1/2, a generalization of the spin-1/2 XXZ Hamiltonian, is also obtained, and the possibility of a supersolid region is discussed.
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