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We show that multi-orbital and density-induced tunneling have a significantimpact on the phase diagram of bosonic atoms in optical lattices. Off-siteinteractions lead to density-induced hopping, the so-called bond-chargeinteractions, which can be identified with an effective tunneling potential andcan reach the same order of magnitude as conventional tunneling. In addition,interaction-induced higher-band processes also give rise to strongly modifiedtunneling, on-site and bond-charge interactions. We derive an extendedoccupation-dependent Hubbard model with multi-orbitally renormalized processesand compute the corresponding phase diagram. It substantially deviates from thesingle-band Bose-Hubbard model and predicts strong changes of the superfluid toMott-insulator transition. In general, the presented beyond-Hubbard physicsplays an essential role in bosonic lattice systems and has an observableinfluence on experiments with tunable interactions.

Multi-orbital and density-induced tunneling of bosons in optical lattices