Non-standard Hubbard models in optical lattices: a review.

@article{Dutta2015NonstandardHM,
  title={Non-standard Hubbard models in optical lattices: a review.},
  author={Omjyoti Dutta and Mariusz Gajda and Philipp Hauke and Maciej Lewenstein and Dirk-S{\"o}ren L{\"u}hmann and Boris A. Malomed and Tomasz Sowiński and Jakub J. Zakrzewski},
  journal={Reports on progress in physics. Physical Society},
  year={2015},
  volume={78 6},
  pages={
          066001
        }
}
Originally, the Hubbard model was derived for describing the behavior of strongly correlated electrons in solids. However, for over a decade now, variations of it have also routinely been implemented with ultracold atoms in optical lattices, allowing their study in a clean, essentially defect-free environment. Here, we review some of the vast literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After giving an introduction to standard (fermionic and… 
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