Ground-state phase diagram of an interacting Bose model with near-neighbor repulsion

We study the ground-state phase diagram of a one-dimensional lattice model of interacting bosons at commensurate filling. When the ratio of interaction strengths to bandwidth is small, the bosons condense into a superfluid phase. For large on-site repulsion, there is a phase transition to a localized Mott phase where the gap Δ is nonzero and the Fourier transform at zero momentum of the density-density correlation function S(q=0) diverges. For large intersite repulsion, S(q=π) diverges first. By examining the superfluid density ${\mathrm{\rho }}_{\mathit{s}}$, in addition to the gap and S(q), we obtain a complete characterization of the phase diagram.