Multiband Effects and the Bose-Hubbard Model in One-Dimensional Lattices

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 $n=1$.

8 pages, 8 figures

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• Accuracy of quantum simulators with ultracold dipolar molecules: a quantitative comparison between continuum and lattice descriptions
• Realizing the Haldane Phase with Bosons in Optical Lattices
• Realizing multiband states with ultracold dipolar quantum simulators
• Competing order in two-band Bose-Hubbard chains with extended-range interactions