Stability of superdiffusion in nearly integrable spin chains

Understand

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 by integrability.
• Here, we argue that these giant quasiparticles remain long-lived, and give divergent contributions to the low-frequency conductivity $\sigma(\omega)$, even in systems that are not perfectly integrable.
• We find, perturbatively, that $ \sigma(\omega) \sim \omega^{-1/3}$ for translation-invariant static perturbations that conserve energy, and $\sigma(\omega) \sim | \log \omega |$ for noisy perturbations.