Robust Kardar-Parisi-Zhang transport in long-range interacting quantum spin chains

The emergence of irreversible classical hydrodynamics from charge-conserving, unitary quantum dynamics represents one of the central tenets of statistical physics. At high temperatures, conserved charges in a generic system are expected to equilibrate diffusively, resembling the motion of a random walk. Recent excitement has focused on a notable exception to diffusion: infinite-temperature spin transport in the integrable, nearest-neighbor quantum Heisenberg chain seems to belong to an as-yet-unidentified dynamical universality class closely related to that of Kardar, Parisi, and Zhang (KPZ). A natural question, partially motivated by experiments is the following: Does KPZ-like transport ever control the physics of quantum dynamics experiments away from fine-tuned, integrable fixed points? In this talk, I will demonstrate the surprising result that nearly all long-range interacting Heisenberg spin chains -- despite a lack of integrability and the asymptotic expectation of diffusion -- exhibit long-lived z = 3/2 superdiffusive spin transport and two-point correlators consistent with KPZ scaling functions, up to very late times ~ 10^3/J. We conjecture that such KPZ-like transport is due to the proximity of such long-range interacting models to the family of so-called Inozemtsev models.