KPZ universality in spin transport of the 1D Heisenberg model

Establish whether Kardar–Parisi–Zhang (KPZ) universality governs spin transport in the one-dimensional Heisenberg spin chain, determining if the transport dynamics and associated statistical properties fall within the KPZ universality class.

Background

The authors discuss the proposal that KPZ universality, known from interface growth in classical systems, may also describe spin transport in the one-dimensional Heisenberg model. This conjecture has been examined experimentally using atomic and superconducting-qubit chains, with mixed support across different moments of magnetization transfer.

The persistence of this conjecture as a debated question motivates precise theoretical and experimental determination of whether Heisenberg-chain spin transport belongs to the KPZ universality class.

References

KPZ universality was also conjectured to describe spin transport in the 1D Heisenberg model based on theoretical evidence.

— Discovering novel quantum dynamics with NISQ simulators (2512.08293 - Roushan et al., 9 Dec 2025) in Category (ii) Testing scientific conjectures; Page 3