The Fate of the Two-Magnon Bound State in the Heisenberg Antiferromagnet

The energy spectrum of the two-magnon bound states in the Heisenberg-Ising antiferromagnet on the square lattice are calculated using series expansion methods. The results confirm an earlier spin-wave prediction of Oguchi and Ishikawa, that the bound states vanish into the continuum before the isotropic Heisenberg limit is reached.