Theory of Two-Magnon Bound States in the Heisenberg Ferro- and Antiferromagnet

A theory for the two-magnon bound state problem is developed for the Heisenberg Hamiltonian with arbitrary spin S and arbitrary dimensionality. The present theory can be applied not only to a ferromagnet but also to an antiferromagnet. It is much simpler and straightforward compared with the many previous theories for the case of ferromagnetism. In the case of antiferromagnetism, the spin-wave approximation must be used. The detailed calculations were carried out for the total wave number K =0, π/2 and π in a one-dimensional antiferromagnet. It was first found that bound states exist outside of the two-magnon band. It is very interesting that the energies of the bound states at K =0 and π are lower than the ground-state energy obtained by the spin-wave theory. This indicates that the antiferromagnetic order is not stable in a one-dimensional lattice.