The Bose–Hubbard model is a theoretical framework used in condensed matter physics to describe the behavior of interacting bosons on a lattice. This model is particularly significant for studying phenomena such as superfluidity and the formation of Bose-Einstein condensates.
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A lattice boson Hamiltonian operator combining hopping and on-site repulsion. The on-site interaction counts distinct particle pairs through . It is the bosonic counterpart of the Hubbard model; projecting a continuum contact interaction onto localized orbitals gives when intersite overlaps are negligible.