Exact solution of the quantum integrable model associated with the twisted D_3^(2) algebra

We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted D_3^(2) algebra (or the 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) model and other high rank integrable models.