Stability of superdiffusion in nearly integrable spin chains

Abstract

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 $\ddot{I}ƒ(\ddot{I}‰)$, even in systems that are not perfectly integrable. We find, perturbatively, that $\ddot{I}ƒ(\ddot{I}‰)\sim \ddot{I}{‰}^{-1/3}$ for translation-invariant static perturbations that conserve energy, and $\ddot{I}ƒ(\ddot{I}‰)\sim |\log \ddot{I}‰|$ 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 nonabelian symmetry yield conventional diffusion. Numerical evidence supports the distinction between these two classes of perturbations.

4 + epsilon pages, 2 figures + 8 pages supp. mat. v3: published version