The one-dimensional extended Bose-Hubbard model

We use the finite-size, density-matrix-renormalization-group(DMRG) method to obtain the zero-temperature phase diagram of the one-dimensional, extended Bose-Hubbard model, for mean boson density ρ=1, in the U-V plane (U and V are respectively, onsite and nearest-neighbour repulsive interactions between bosons). The phase diagram includes superfluid (SF), bosonic-Mott-insulator(MI), and mass-density-wave (MDW) phases. We determine the natures of the quantum phase transitions between these phases