Two-magnon problem in linear anisotropic spin chains with an arbitrary radius of interaction

Bound two-magnon states cannot exist in the XY-spin model with an arbitrary radius of bilinear exchange interaction, S ⪖ 12. In the Ising model with bilinear and biquadratic interaction, however, as well as in every anisotropic model at κ = π, the bound states number is n + 1 (n at S = 12), where n is the number of the ZZ interacting neighbours. In every anisotropic model with nearest-neighbour XY interaction only the bound states number at different points of the Brillouin zone is not greater than n + 1.