Condensed Matter > Statistical Mechanics
[Submitted on 3 Feb 2021 (v1), last revised 1 Aug 2021 (this version, v3)]
Title:Stability of superdiffusion in nearly integrable spin chains
View PDFAbstract: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.
Submission history
From: Romain Vasseur [view email][v1] Wed, 3 Feb 2021 19:00:04 UTC (587 KB)
[v2] Mon, 1 Mar 2021 13:53:56 UTC (662 KB)
[v3] Sun, 1 Aug 2021 13:42:21 UTC (671 KB)
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