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

Wei Xu, Maxim Olshanii, Marcos Rigol

Abstract: 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.