  We show that multi-orbital and density-induced tunneling have a significant
impact on the phase diagram of bosonic atoms in optical lattices. Off-site
interactions lead to density-induced hopping, the so-called bond-charge
interactions, which can be identified with an effective tunneling potential and
can reach the same order of magnitude as conventional tunneling. In addition,
interaction-induced higher-band processes also give rise to strongly modified
tunneling, on-site and bond-charge interactions. We derive an extended
occupation-dependent Hubbard model with multi-orbitally renormalized processes
and compute the corresponding phase diagram. It substantially deviates from the
single-band Bose-Hubbard model and predicts strong changes of the superfluid to
Mott-insulator transition. In general, the presented beyond-Hubbard physics
plays an essential role in bosonic lattice systems and has an observable
influence on experiments with tunable interactions.
