In the continuum O(3) $\sigma$-model description of gapped spin systems, $S=1$ magnons can only decay into three lower energy magnons. We argue that the symmetry of the quantum spin Hamiltonian often allows decay into two magnons, and compute this decay rate in model systems. Two-magnon decay is present in Haldane gap $S=1$ spin chains, even though it cannot be induced by any allowed term written in powers and gradients of the $\sigma$-model field. We compare our results with recent measurements of Stone et al. on a two-dimensional spin system.

• Received 22 November 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.087203