Phases of the one-dimensional Bose-Hubbard model

The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with nearest-neighbor interaction is investigated using the density-matrix renormalization group. Recently normal phases without long-range order have been conjectured between the charge-density wave phase and the superfluid phase in one-dimensional bosonic systems without disorder. Our calculations demonstrate that there is no intermediate phase in the one-dimensional Bose-Hubbard model but a simultaneous vanishing of crystalline order and appearance of superfluid order. The complete phase diagrams with and without nearest-neighbor interaction are obtained. Both phase diagrams show reentrance from the superfluid phase to the insulator phase.