Slow crossover from superdiffusion to diffusion in isotropic spin chains

Finite-temperature spin transport in integrable isotropic spin chains (i.e., spin chains with continuous nonabelian symmetries) is known to be superdiffusive, with anomalous transport properties displaying remarkable robustness to isotropic integrability-breaking perturbations. Using a discrete-time classical model, we numerically study the crossover to conventional diffusion resulting from both noisy and Floquet isotropic perturbations of strength λ. We identify an anomalously-long crossover time scale t_⋆∼λ^-α with α≈ 6 in both cases. We discuss our results in terms of a kinetic theory of transport that characterizes the lifetimes of large solitons responsible for superdiffusion.