Superdiffusion is surprisingly easily observed even in systems without the integrability underpinning this phenomenon. Indeed, the classical Heisenberg chain-one of the simplest many-body systems, and firmly believed to be nonintegrable-evinces a long-lived regime of anomalous, superdiffusive spin dynamics at finite temperature. Similarly, superdiffusion persists for long timescales, even at high temperature, for small perturbations around a related integrable model. Eventually, however, ordinary diffusion is believed to be asymptotically restored. We examine the timescales governing the lifetime of the superdiffusive regime, and argue that it diverges algebraically fast-both in deviation from the integrable limit, and at low temperature, where we find t^{*}∼T^{-ζ} with an exponent possibly as large as ζ=8. This can render the crossover to ordinary diffusion practically inaccessible.
Finite-temperature spin transport in integrable isotropic spin chains (i.e., spin chains with continuous non-Abelian 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 $\ensuremath{\lambda}$. We identify an anomalously-long crossover timescale ${t}_{★}\ensuremath{\sim}{\ensuremath{\lambda}}^{\ensuremath{-}\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\approx}6$ 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.
Observing superdiffusive scaling in the spin transport of the integrable 1D Heisenberg model is one of the key discoveries in non-equilibrium quantum many-body physics. Despite this remarkable theoretical development and the subsequent experimental observation of the phenomena in KCuF
3, real materials are often imperfect and contain integrability breaking interactions. Understanding the effect of such terms on the superdiffusion is crucial in identifying connections to such materials. Current quantum hardware has already ascertained its utility in studying such non-equilibrium phenomena by simulating the superdiffusion of the 1D Heisenberg model. In this work, we perform a quantum simulation of the superdiffusion breakdown by generalizing the superdiffusive Floquet-type 1D Heisenberg model to a general 2D model. We comprehensively study the effect of different 2D interactions on the superdiffusion breakdown by tuning up their strength from zero, corresponding to the 1D Heisenberg chain, to finite nonzero values. We observe that certain 2D interactions are more resilient against superdiffusion breakdown than others and that the
SU(2) preserving 2D interaction has the highest resilience among all the 2D interactions we study. Importantly, this observed resilience has direct implications for sustaining superdiffusive spin transport in two-dimensional lattices. We reason out the relative resilience against the superdiffusion breakdown through an analysis of the scattering coefficients off the 2D interaction in otherwise 1D chains. The relative resilience of different interaction types against superdiffusion breakdown was also captured in quantum hardware with remarkable accuracy, further establishing the current quantum hardware's applicability in simulating interesting non-equilibrium quantum many-body phenomena.