Exact solution of the two-axis two-spin Hamiltonian

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