Slow crossover from superdiffusion to diffusion in isotropic spin chains

Abstract

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 $\lambda$. We identify an anomalously-long crossover time scale $t_{\star }\sim {\lambda }^{-\alpha }$ with $\alpha \approx 6$ 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.

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• Superdiffusion resilience in Heisenberg Chains with 2D interactions on a quantum processor
• Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems