标题： Kardar-Parisi-Zhang标度在具有破坏可积性的经典可积自旋链中的鲁棒性 显示英文标题

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

摘要： 最近的研究观察到了可积的经典和量子自旋链中的超扩散现象。这些自旋链与Kardar-Parisi-Zhang (KPZ)普适性类之间出现了一个引人入胜的联系。理论发展（例如广义流体力学）强调了可积性以及自旋对称性在KPZ行为中的作用。然而，理解它们在超扩散传输中的精确作用仍然是一项具有挑战性的任务。广泛使用的量子自旋链平台存在严重的数值限制。为了克服这一障碍，我们关注一个经典可积自旋链，该链被证明与量子自旋-$\frac{1}{2}$海森堡链有深刻的类比关系。值得注意的是，我们发现即使考虑破坏可积性但保持自旋对称性的项，KPZ行为仍然占主导地位，这强烈表明自旋对称性在非微扰区域中起着核心作用。另一方面，在非微扰区域，我们发现能量相关性表现出明显的扩散行为。我们还研究了时间有序关联函数（OTOC）的经典对应物和李雅普诺夫指数。我们发现，对于破坏可积性的案例，混沌的存在显著，尽管KPZ行为仍然具有鲁棒性。KPZ行为的鲁棒性已在一类保持自旋对称性的可积性破坏项中得到展示。 显示英文摘要

摘要： 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.