Integrable model of bosons in a four-well ring with anisotropic tunneling

We introduce an integrable, four-well ring model for bosons where the tunneling couplings between nearest-neighbour wells are not restricted to be equal. We show how the model may be derived through the quantum inverse scattering method from a solution of the Yang-Baxter equation, and in turn solved by algebraic Bethe ansatz means. The model admits multiple pseudo-vacuum states. Numerical evidence is provided to indicate that all pseudo-vacua are required to obtain a complete set of Bethe eigenstates. The model has the notable property that there is a class of eigenstates which admit a simple, closed-form energy expression.