Stability of superdiffusion in nearly integrable spin chains
Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur, Brayden Ware
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
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 nonabelian symmetry yield conventional diffusion. Numerical evidence supports the distinction between these two classes of perturbations.