Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains

TL;DR

This paper demonstrates that the Kardar-Parisi-Zhang universality class partially emerges in integrable isotropic spin chains, confirmed through extensive numerical simulations aligning with KPZ scaling laws, even with energy currents present.

Contribution

It provides the first comprehensive numerical evidence of KPZ scaling in isotropic spin chains, clarifying previous discrepancies and establishing a partial KPZ universality in these systems.

Findings

Full agreement with KPZ scaling laws in spin chains

KPZ laws remain valid with energy currents when properly boosted

Numerical simulations confirm partial KPZ emergence in isotropic spin chains

Abstract

Integrable spin chains with a continuous non-Abelian symmetry, such as the one-dimensional isotropic Heisenberg model, show superdiffusive transport with little theoretical understanding. Although recent studies reported a surprising connection to the Kardar-Parisi-Zhang (KPZ) universality class in that case, this view was most recently questioned by discrepancies in full counting statistics. Here, by combining extensive numerical simulations of classical and quantum integrable isotropic spin chains with a framework developed by exact studies of the KPZ class, we characterize various two-point quantities that remain hitherto unexplored in spin chains, and find full agreement with KPZ scaling laws without adjustable parameters. This establishes the partial emergence of the KPZ class in integrable isotropic spin chains. Moreover, we reveal that the KPZ scaling laws are intact in the presence of an energy current, under the appropriate Galilean boost required by the propagation of spacetime correlation.