A carefully tuned three-site extended Bose-Hubbard model with nearest-neighbour interactions is integrable and solved exactly by a Bethe ansatz.
Twisting singular solutions of Bethe's equations
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abstract
The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.
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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.