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We study one-dimensional truncated (no more than 2 particles on a site)bosonic Hubbard model in both repulsive and attractive regimes by exactdiagonalization and exact worldline Monte Carlo simulation. In the commensuratecase (one particle per site) we demonstrate that the point of Mott-insulator --superfluid transition, $(U/t)_c=0.50\pm 0.05$, is remarkably far from that ofthe full model. In the attractive region we observe the phase transition fromone-particle superfluid to two-particle one. The paring gap demonstrates alinear behavior in the vicinity of the critical point. The critical statefeatures marginal response to the gauge phase. We argue that the two-particlesuperfluid is a macroscopic analog of a peculiar phase observed earlier in aspin-1 model with axial anisotropy.Comment: Revtex, 5 pages, 9 figures. Submitted to Phys. Rev.

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