The algebraic Bethe ansatz is formulated for the one-dimensional Bariev chain. As a consequence, the eigenvectors, eigenvalues and Bariev's Bethe equations are rederived in a systematic algebraic way.
The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N sites have solutions containing ±i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions must be carefully regularized. We consider a regularization involving a parameter that can be determined using a generalization of the Bethe equations. These generalized Bethe equations provide a practical way of determining which singular solutions correspond to eigenvectors of the model.