Exact solution of the alternating XXZ spin chain with generic non-diagonal boundaries

The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal KK-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused RR-matrices and KK-matrices, we obtain certain closed operator identities and conditions, which allow us to construct an inhomogeneous T−QT−Q relation and the associated Bethe Ansatz equations accounting for the eigenvalues of the transfer matrix.