Quantum integrable multi-well tunneling models

In this work we present a general construction of integrable models describing boson tunneling in multi-well systems. We show how the models may be derived through the quantum inverse scattering method and solved by algebraic Bethe ansatz means. From the transfer matrix we find only two conserved operators. However, we construct additional conserved operators through an alternative approach. As a consequence the models admit multiple pseudovacua, each associated with a set of Bethe ansatz equations (BAEs). We show that all sets of BAEs are needed to obtain a complete set of eigenstates.