Universal Kardar-Parisi-Zhang dynamics in integrable spin chains

Recent advances in the control and manipulation of ultracold atoms in optical lattices have opened the door to studying SU(N)-symmetric spin models. This offers the tantalizing opportunity to study the dynamics of a wide variety of one dimensional integrable models where the interplay between integrability and symmetry leads to anomalous transport. Leveraging a novel numerical technique, termed density matrix truncation, we show that transport in these systems can be superdiffusive, and moreover fall into the Kardar–Parisi–Zhang (KPZ) universality class. This combines and generalizes previous theoretical and experimental results to SU(N) symmetric models, as well as to other non-Abelian symmetric models, their periodically driven counterparts, and supersymmetric analogues. By exploiting optical pumping, we discuss how to experimentally generate the spatially inhomogeneous, near infinite-temperature initial state required to study this novel KPZ transport. Moreover, we demonstrate how such transport can be identified from the spatial profile of polarization using current state-of-the-art single-shot detection with single-site spatial resolution.