Exact solution of the two-axis two-spin Hamiltonian

Bethe ansatz solution of the two-axis two-spin Hamiltonian is derived based on Jordan-Schwinger boson realization SU(2) algebra. It shown that equations can be obtained as zeros related extended Heine-Stieltjes polynomials. Symmetry properties excited levels system and polynomials are discussed. As an example application theory, two equal spin case studied in detail, which demonstrates each band symmetric with respect to zero energy plane perpendicular level diagram states always well entangled.