Integrable 3-Site, Tilted, Extended Bose-Hubbard Model with Nearest-Neighbour Interactions

Extended Bose-Hubbard models have been employed in the study of cold-atom systems with dipolar interactions. It is shown that, for a certain choice of the coupling parameters, there exists an integrable extended 3-site Bose-Hubbard model with nearest-neighbour interactions. A Bethe ansatz procedure is developed to obtain expressions for the energy spectrum and eigenstates.