Stability of Superdiffusion in Nearly Integrable Spin Chains

Superdiffusive finite-temperature transport has been recently observed in a variety of integrable systems with non-Abelian 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 σ(ω), even in systems that are not perfectly integrable. We find, perturbatively, that σ(ω)∼ω-1/3 for translation-invariant static perturbations that conserve energy and σ(ω)∼|logω| for noisy perturbations. The (presumable) crossover to regular diffusion appears to lie beyond low-order perturbation theory. By contrast, integrability-breaking perturbations that break the non-Abelian symmetry yield conventional diffusion. Numerical evidence supports the distinction between these two classes of perturbations.