Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
Dipankar Roy, Abhishek Dhar, Herbert Spohn, Manas Kulkarni
Abstract
Recent investigations have observed superdiffusion in integrable classical and quantum spin chains. An intriguing connection between these spin chains and the 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 behavior. 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 a deep analogy with the quantum spin-$\frac{1}{2}$ Heisenberg chain. Remarkably, we find that KPZ behavior prevails even when one considers integrability-breaking but spin-symmetry preserving terms, strongly indicating that spin symmetry plays a central role even in the nonperturbative regime. On the other hand, in the nonperturbative regime, we find that energy correlations exhibit clear diffusive behavior. We also study the classical analog of the out-of-time-ordered correlator and Lyapunov exponents. We find a significant presence of chaos for the integrability-broken cases even though KPZ behavior remains robust. The robustness of KPZ behavior is demonstrated for a wide class of spin-symmetry preserving integrability-breaking terms.