Stability of Superdiffusion in Nearly Integrable Spin Chains

Superdiffusive finite-temperature transport has been recently observed in a variety of integrable systems with nonabelian global symmetries. Superdiffusion is caused by giant Goldstone-like quasiparticles stabilized integrability. Here, we argue that these remain long-lived, and give divergent contributions to the low-frequency conductivity $\sigma(\omega)$, even are not perfectly integrable. We find, perturbatively, $ \sigma(\omega) \sim \omega^{-1/3}$ for translation-invariant static perturbations conserve energy, $\sigma(\omega) | \log \omega |$ noisy perturbations. The (presumable) crossover regular diffusion appears lie beyond low-order perturbation theory. By contrast, integrability-breaking break symmetry yield conventional diffusion. Numerical evidence supports distinction between two classes