Zero-point phase transitions in the one-dimensional truncated bosonic Hubbard model and its spin-1 analog

We study ground-state properties of the one-dimensional truncated (no more than two particles on a site) bosonic Hubbard model in both repulsive and attractive regimes by exact diagonalization and exact world-line Monte Carlo simulation. In the commensurate case (one particle per site) we demonstrate that the point of Mott-insulator–superfluid transition, ${\mathrm{}(U/t)\mathrm{}}_c=0.50\mathrm{}\pm 0.05$, is remarkably far from that of the full model. In the attractive region we observe the phase transition from a one-particle superfluid to a two-particle one. The paring gap demonstrates a linear behavior in the vicinity of the critical point. The critical state features marginal response to the gauge phase. We argue that the two-particle superfluid is a macroscopic analog of a peculiar phase observed earlier in a spin-1 model with axial anisotropy.