Spectrum of the quantum integrable $D^{(2)}_2$ spin chain with generic boundary fields

Abstract: Exact solution of the quantum integrable $D^{(2)}_2$ spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered anisotropic XXZ spin chains. Based on this identity, the eigenvalues and Bethe ansatz equations of the $D^{(2)}_2$ model are derived via off-diagonal Bethe ansatz.