Stability of superdiffusion in nearly integrable spin chains

TL;DR

This paper investigates how superdiffusive transport persists in nearly integrable spin chains, showing that giant quasiparticles cause divergent conductivity contributions even with small perturbations, contrasting with normal diffusion under symmetry-breaking perturbations.

Contribution

It demonstrates that superdiffusive behavior remains robust under certain perturbations and characterizes the divergence of conductivity, providing a perturbative analysis and numerical evidence.

Findings

Superdiffusion persists with divergent conductivity contributions.

Perturbative analysis shows specific frequency dependence of conductivity.

Symmetry-breaking perturbations lead to conventional diffusion.

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 $\sigma(\omega)$, 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. 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.