Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability

TL;DR

This study demonstrates that Kardar-Parisi-Zhang (KPZ) scaling persists in a classical integrable spin chain even when integrability is broken but spin-symmetry is preserved, highlighting the central role of spin-symmetry in superdiffusive transport.

Contribution

It shows that KPZ universality is robust against integrability-breaking perturbations in a classical spin chain, emphasizing the importance of spin-symmetry in superdiffusive behavior.

Findings

KPZ behaviour persists despite integrability-breaking terms.

Energy correlations become diffusive in non-perturbative regimes.

Chaos is present even when KPZ scaling remains robust.

Abstract

Recent investigations have observed superdiffusion in integrable classical and quantum spin chains. An intriguing connection between these spin chains and Kardar-Parisi-Zhang (KPZ) universality class has emerged. Theoretical developments (e.g. generalized hydrodynamics) have highlighted the role of integrability as well as spin-symmetry in KPZ behaviour. However understanding their precise role on superdiffusive transport still remains a challenging task. The widely used quantum spin chain platform comes with severe numerical limitations. To circumvent this barrier, we focus on a classical integrable spin chain which was shown to have deep analogy with the quantum spin-$\frac{1}{2}$ Heisenberg chain. Remarkably, we find that KPZ behaviour prevails even when one considers integrability-breaking but spin-symmetry preserving terms, strongly indicating that spin-symmetry plays a central role even in the non-perturbative regime. On the other hand, in the non-perturbative regime, we find that energy correlations exhibit clear diffusive behaviour. We also study the classical analog of out-of-time-ordered correlator (OTOC) and Lyapunov exponents. We find significant presence of chaos for the integrability-broken cases even though KPZ behaviour remains robust. The robustness of KPZ behaviour is demonstrated for a wide class of spin-symmetry preserving integrability-breaking terms.