Anomalous T=∞ transport in 1D long-range spin chains proximate to integrability

Recent analytic, numerical, and experimental results have demonstrated that integrability and non-Abelian symmetry give rise to anomalous, non-diffusive behavior in high-temperature quantum transport. To understand the applicability of such fine-tuned results to atomic platforms, we study infinite-temperature spin and energy transport in long-range, interacting spin chains using state-of-the-art tensor network simulations. First, we consider two model families that interpolate between the superdiffusive nearest-neighbor Heisenberg and ballistic Haldane-Shastry models: non-integrable power-law and integrable Inozemtsev models. For power-law models, in contrast to the expected diffusion, we find long-lived z=3/2 superdiffusive spin transport and ballistic energy transport up to times t∼400/J. This KPZ-like behavior is explained by the proximity of power-law models to integrable Inozemtsev models, which also display z=3/2 superdiffusive spin transport and several properties of the Kardar-Parisi-Zhang universality class, as has been found for the nearest-neighbor model. Finally, we consider anisotropic, non-integrable spin models motivated by Rydberg atom and ultracold polar molecule platforms, demonstrating that a wide range of long-lived, non-diffusive transport can be observed in experimental settings even when both integrability and SU(2) symmetry are broken.