Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems

TL;DR

This paper provides extensive numerical evidence that KPZ universality governs high-temperature spin transport in a broad class of integrable quantum systems, including various symmetries and driven models, with implications for experimental realizations.

Contribution

It demonstrates that KPZ dynamics are universal in integrable quantum spin chains with non-Abelian symmetry and extends this to supersymmetric and periodically-driven models.

Findings

KPZ universality class describes spin transport in Heisenberg model.

KPZ dynamics observed in supersymmetric and driven models.

Proposed experimental protocol for observing KPZ scaling in optical lattices.

Abstract

Although the Bethe ansatz solution of the spin-1/2 Heisenberg model dates back nearly a century, the anomalous nature of its high-temperature transport dynamics has only recently been uncovered. Indeed, numerical and experimental observations have demonstrated that spin transport in this paradigmatic model falls into the Kardar-Parisi-Zhang (KPZ) universality class. This has inspired the significantly stronger conjecture that KPZ dynamics, in fact, occur in all integrable spin chains with non-Abelian symmetry. Here, we provide extensive numerical evidence affirming this conjecture. Moreover, we observe that KPZ transport is even more generic, arising in both supersymmetric and periodically-driven models. Motivated by recent advances in the realization of SU(N)-symmetric spin models in alkaline-earth-based optical lattice experiments, we propose and analyze a protocol to directly investigate the KPZ scaling function in such systems.