We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse settings ranging from hot nuclear matter to cold atomic gases and quantum spin chains. In every dimension and for every flavor symmetry group, the low energy theory is a set of coupled noisy diffusion equations. Independence of the physics on the choice of canonical or microcanonical ensemble is manifest in our hydrodynamic expansion, even though the ensemble choice causes an apparent shift in quasinormal mode spectra. We use our formalism to explain why flavor symmetry is qualitatively different from hydrodynamics with other non-Abelian conservation laws, including angular momentum and charge multipoles. As a significant application of our framework, we study spin and energy diffusion in classical one-dimensional SU(2)-invariant spin chains, including the Heisenberg model along with multiple generalizations. We argue based on both numerical simulations and our effective field theory framework that non-integrable spin chains on a lattice exhibit conventional spin diffusion, in contrast to some recent predictions that diffusion constants grow logarithmically at late times. We show that the apparent enhancement of diffusion is due to slow equilibration caused by (non-Abelian) hydrodynamic fluctuations.

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具有连续非阿贝尔对称性的晶格模型中的流体动力学

我们为具有整体连续非阿贝尔对称性的晶格上的多体系统开发了系统的流体力学有效场论。具有连续非阿贝尔对称性的模型在物理学中无处不在，它出现在从热核物质到冷原子气体和量子自旋链的各种环境中。在每个维度和每个风味对称性组中，低能量理论都是一组耦合的噪声扩散方程。尽管我们的流体动力学扩展表明，物理学对正则或微正则集合体选择的独立性是显而易见的，即使集合体选择引起准法向谱的明显变化也是如此。我们用形式主义来解释为什么风味对称性与其他非阿贝尔守恒定律（包括角动量和电荷多极子）的流体力学在质量上有区别。作为我们框架的重要应用，我们研究了经典一维SU（2）不变自旋链中的自旋和能量扩散，包括Heisenberg模型以及多种概化。我们基于数值模拟和有效场论框架都认为，晶格上不可整合的自旋链表现出常规的自旋扩散，这与最近的一些预测（扩散常数在对数末期增长）相反。我们表明，扩散的明显增强是由于（非阿贝尔）水动力波动引起的缓慢平衡所致。我们基于数值模拟和有效场论框架都认为，晶格上不可整合的自旋链表现出常规的自旋扩散，这与最近的一些预测（扩散常数在对数末期增长）相反。我们表明，扩散的明显增强是由于（非阿贝尔）水动力波动引起的缓慢平衡所致。我们基于数值模拟和有效场论框架都认为，晶格上不可整合的自旋链表现出常规的自旋扩散，这与最近的一些预测（扩散常数在对数末期增长）相反。我们表明，扩散的明显增强是由于（非阿贝尔）水动力波动引起的缓慢平衡所致。