Timescales of superdiffusion in non-integrable spin chains

The classical Heisenberg chain is one of the simplest many-body models of magnetism, but, despite this apparent simplicity - and the fact that it is a non-integrable system - it evinces a long-lived regime of anomalous, superdiffusive spin dynamics at finite temperature. We examine the temperature-dependence of the lifetime of the superdiffusive regime, and present an argument that it diverges at low temperature - rendering the expected crossover to ordinary diffusion practically inaccessible - and show that numerical simulations of the finite-temperature dynamics are in agreement with this picture.