Anomalous transport in isotropic spin chains with broken integrability

Transport in high-temperature quantum spin chains is generally expected to be incoherent and diffusive; however, in recent years, superdiffusive spin transport has numerically and experimentally been observed in isotropic spin chains. While the precise mechanism underpinning superdiffusive spin transport has yet to be understood in detail, a growing body of theoretical and numerical work has established an intimate link between a system's proximity to integrability and spin superdiffusion. When integrability is broken, spin transport eventually becomes diffusive; presently, the nature of this return to diffusion, including the relevant timescales and their relationship to the strength of the integrability-breaking perturbation, are not well understood. In this work, we employ an classical, discrete-time numerical model to study this superdiffusive-to-diffusive crossover as well as its relation to conservation of energy and preservation of spin-rotation symmetry.