Robustness of Kardar-Parisi-Zhang-like transport in long-range interacting quantum spin chains

TL;DR

This paper demonstrates that long-range Heisenberg spin chains exhibit persistent KPZ-like superdiffusive transport, extending findings from integrable models to more generic, non-integrable systems relevant for quantum simulation.

Contribution

It shows that non-integrable, long-range Heisenberg models display KPZ-like superdiffusive transport, linked to proximity to integrable Inozemtsev models, with implications for experimental quantum systems.

Findings

Long-lived superdiffusive spin transport with z=3/2 observed in power-law models

KPZ scaling functions are consistent with two-point correlators up to t ~ 10^3/J

KPZ-like transport persists across all interaction ranges in Inozemtsev models

Abstract

Isotropic integrable spin chains such as the Heisenberg model feature superdiffusive spin transport belonging to an as-yet-unidentified dynamical universality class closely related to that of Kardar, Parisi, and Zhang (KPZ). To determine whether these results extend to more generic one-dimensional models, particularly those realizable in quantum simulators, we investigate spin and energy transport in non-integrable, long-range Heisenberg models using state-of-the-art tensor network methods. Despite the lack of integrability and the asymptotic expectation of diffusion, for power-law models (with exponent $2 < \alpha < \infty$) we observe long-lived $z=3/2$ superdiffusive spin transport and two-point correlators consistent with KPZ scaling functions, up to times $t \sim 10^3/J$. We conjecture that this KPZ-like transport is due to the proximity of such power-law-interacting models to the integrable family of Inozemtsev models, which we show to also exhibit KPZ-like spin transport across all interaction ranges. Finally, we consider anisotropic spin models naturally realized in Rydberg atom arrays and ultracold polar molecules, demonstrating that a wide range of long-lived, non-diffusive transport can be observed in experimental settings.