Exact spectrum of the spin-s Heisenberg chain with generic non-diagonal boundaries

The off-diagonal Bethe ansatz method is generalized to the high spin integrable systems associated with the su(2) algebra by employing the spin-s isotropic Heisenberg chain model with generic integrable boundaries as an example. With the fusion techniques, certain closed operator identities for constructing the functional T - Q relations and the Bethe ansatz equations are derived. It is found that a variety of inhomogeneous T - Q relations obeying the operator product identities can be constructed. Numerical results for two-site s = 1 case indicate that an arbitrary choice of the derived T - Q relations is enough to give the complete spectrum of the transfer matrix.