Abstract
Quantum systems of particles obeying Bose statistics and moving in d-dimensional lattices are studied. The original Bose–Hubbard Hamiltonian is considered, together with model systems related to this Hamiltonian: the Bose–Hubbard model with exchange interaction of infinite radius and the Bose–Hubbard model with infinite interaction potential. Rigorous results concerning the proof of the existence of Bose condensation and a phase transition to the Mott insulator state in these systems are presented.
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