Multiband effects and the Bose-Hubbard model in one-dimensional lattices

We study phase diagrams of one-dimensional bosons with contact interactions in the presence of a lattice. We use the worm algorithm in continuous space and focus on the incommensurate superfluid-Mott-insulator transition. Our results are compared to those from the one-band Bose-Hubbard model. When Wannier states are used to determine the Bose-Hubbard model parameters, the comparison unveils an apparent breakdown of the one-band description for strong interactions, even for the Mott-insulating state with an average of one particle per site (n=1) in deep lattices. We introduce an inverse confined scattering analysis to obtain the ratio U/J, with which the Bose-Hubbard model provides correct results for strong interactions, deep lattices, and n=1.