The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is subballistic at any nonzero temperature: An initially localized spin fluctuation spreads in time t to a width t2/3. This exponent as well as the functional form of the dynamical spin correlation function suggest that spin transport is in the Kardar–Parisi–Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.

中文翻译：

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近可积系统中非阿贝尔对称性的超扩散


海森堡自旋链是一个规范的可积模型。因此，它具有稳定的弹道传播准粒子，但自旋输运在任何非零温度下都是亚弹道的：初始局部自旋涨落在时间 t 中扩散到宽度 t2/3。该指数以及动态自旋相关函数的函数形式表明自旋输运属于 Kardar-Parisi-Zhang (KPZ) 普遍性类别。然而，磁化强度的完整计数统计显然与 KPZ 缩放不兼容。从微观原理推导出来的简单双模式流体动力学描述捕获了相关函数的 KPZ 缩放和完整计数统计的粗略特征，但仍有待数值验证。这些结果可推广到连续非阿贝尔对称下的任何可积自旋链不变量，并且对于尊重非阿贝尔对称性的中等强度的可积破坏扰动具有惊人的鲁棒性。