Exact solution of the quantum integrable model associated with the twisted $$ {\mathrm{D}}_3^{(2)} $$ algebra

Abstract

We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $$ {D}_3^{(2)} $$ D 3 2 algebra (or the $$ {D}_3^{(2)} $$ D 3 2 model) with either periodic or integrable open boundary conditions. We obtain the intrinsic operator product identities among the fused transfer matrices and find a way to close the recursive fusion relations, which makes it possible to determinate eigenvalues of transfer matrices with an arbitrary anisotropic parameter η. Based on them, and the asymptotic behaviors and values at certain points, we construct eigenvalues of transfer matrices in terms of homogeneous T − Q relations for the periodic case and inhomogeneous ones for the open case with some off-diagonal boundary reflections. The associated Bethe ansatz equations are also given. The method and results in this paper can be generalized to the $$ {D}_{n+1}^{(2)} $$ D n + 1 2 model and other high rank integrable models.