Anomalous spin-wave excitations in a one-dimensional Dzyaloshinski--Moriya antiferromagnet

The dynamics of a one-dimensional Heisenberg antiferromagnet with a small Dzyaloshinski--Moriya component to the exchange interaction is considered. The spin rotational invariance within the easy plane is broken by the application of a weak magnetic field in the easy plane. The nature of the spin-wave excitations of the quantum spin system is investigated, and pronounced anomalies in the single-spin-wave spectrum at fields comparable to the anisotropy in the exchange interaction are found. These anomalies are of quantum character and are related to the resonance between the single-spin-wave and the two-spin-wave excitations. The implications for the two-spin-wave bound states are discussed