Anomalous finite-temperature transport has recently been observed in numerical studies of various integrable models in one dimension; these models share the feature of being invariant under a continuous non-Abelian global symmetry. This work offers a comprehensive group-theoretic account of this elusive phenomenon. For an integrable quantum model with local interactions, invariant under a global non-Abelian simple Lie group $G$, we find that finite-temperature transport of Noether charges associated with symmetry $G$ in thermal states that are invariant under $G$ is universally superdiffusive and characterized by the dynamical exponent $z=3/2$. This conclusion holds regardless of the Lie algebra symmetry, local degrees of freedom (on-site representations), Lorentz invariance, or particular realization of microscopic interactions: We accordingly dub it “superuniversal.” The anomalous transport behavior is attributed to long-lived giant quasiparticles dressed by thermal fluctuations. We provide an algebraic viewpoint on the corresponding dressing transformation and elucidate formal connections to fusion identities amongst the quantum-group characters. We identify giant quasiparticles with nonlinear soliton modes of classical field theories that describe low-energy excitations above ferromagnetic vacua. Our analysis of these field theories also provides a complete classification of the low-energy (i.e., Goldstone-mode) spectra of quantum isotropic ferromagnetic chains.

中文翻译：

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超扩散的超普遍性

最近在一维的各种可积模型的数值研究中观察到了异常的有限温度输运；这些模型具有在连续非阿贝尔全局对称性下不变的特征。这项工作为这种难以捉摸的现象提供了全面的群论解释。对于具有局部相互作用的可积量子模型，在全局非阿贝尔简单李群下不变$G$，我们发现与对称性相关的 Noether 电荷的有限温度输运 $G$ 在不变的热状态下 $G$ 是普遍超扩散的，并以动态指数为特征 $z=3/2$. 无论李代数对称性、局部自由度（现场表示）、洛伦兹不变性或微观相互作用的特定实现如何，该结论都成立：我们因此将其称为“超普遍性”。异常的传输行为归因于被热波动修饰的长寿命巨型准粒子。我们提供了有关相应修整变换的代数观点，并阐明了与量子群特征之间融合身份的形式联系。我们确定了具有经典场论非线性孤子模式的巨型准粒子，这些模式描述了铁磁真空上方的低能激发。我们对这些场论的分析还提供了对量子各向同性铁磁链的低能（即戈德斯通模式）光谱的完整分类。