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

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