A natural description of ultracold gases trapped in optical lattices is given by the so-called Hubbard model characterized by the single-particle tunneling rate, on-site and long-range interaction strengths. In this presentation we will talk about interaction-induced extension of such models, namely correlated intra- and inter-orbital tunneling and renormalized interactions.As concrete examples, we will describe how such terms can give rise to novel phases in ultracold dipolar systems.
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