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One-dimensional Bose gas with contact interaction in optical lattices at zerotemperature is investigated by means of the exact diffusion Monte Carloalgorithm. The results obtained from the fundamental continuous model arecompared with those obtained from the lattice (discrete) Bose-Hubbard model,using exact diagonalization, and from the quantum sine-Gordon model. We map outthe complete phase diagram of the continuous model and determine the regions ofapplicability of the Bose-Hubbard model. Various physical quantitiescharacterizing the systems are calculated and it is demonstrated that thesine-Gordon model used for shallow lattices is inaccurate.

One-dimensional Bose gas in optical lattices of arbitrary strength