A carefully tuned three-site extended Bose-Hubbard model with nearest-neighbour interactions is integrable and solved exactly by a Bethe ansatz.
Quantum Chaos in the Bose-Hubbard model
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We present a numerical study of the spectral properties of the 1D Bose-Hubbard model. Unlike the 1D Hubbard model for fermions, this system is found to be non-integrable, and exhibits Wigner-Dyson spectral statistics under suitable conditions.
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Integrable 3-Site, Tilted, Extended Bose-Hubbard Model with Nearest-Neighbour Interactions
A carefully tuned three-site extended Bose-Hubbard model with nearest-neighbour interactions is integrable and solved exactly by a Bethe ansatz.