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We analyze the stability of spin spiral states in the two-dimensionalHeisenberg model. Our analysis reveals that the SU(2) symmetric point hosts adynamic instability that is enabled by the existence of energetically favorabletransverse deformations---both in real and spin space---of the spiral order.The instability is universal in the sense that it applies to systems with anyspin number, spiral wavevector, and spiral amplitude. Unlike the Landau ormodulational instabilities which require impurities or periodic potentialmodulation of an optical lattice, quantum fluctuations alone are sufficient totrigger the transverse instability. We analytically find the most unstable modeand its growth rate, and compare our analysis with phase space methods. Byadding an easy plane exchange coupling that reduces the Hamiltonian symmetryfrom SU(2) to U(1), the stability boundary is shown to continuously interpolatebetween the modulational instability and the transverse instability. Thissuggests that the transverse instability is an important mechanism that hindersthe formation of a spin superfluid, even in the presence of strong exchangeanisotropy.

Transverse instability and universal decay of spin spiral order in the Heisenberg model