Superuniversality of Superdiffusion
Superuniversality of Superdiffusion
复制标题
DOI：
10.1103/physrevx.11.031023
复制
发表时间：
2021-07-28
影响因子：
12.5
通讯作者：
Ware, Brayden
中科院分区：
文献类型：
--
作者：
Ilievski, Enej;De Nardis, Jacopo;Ware, Brayden
反常的有限温度输运最近在一维的各种可积模型的数值研究中被观察到，这些模型具有连续非阿贝尔全局对称下不变的特征。这项工作提供了一个全面的群论帐户这一难以捉摸的现象。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G下不变，我们发现与对称性G相关的Noether电荷在G下不变的热态中的有限温度输运是普遍超扩散的，其特征在于动力学指数z = 3/2。无论李代数对称性、局部自由度（在位表示）、洛伦兹不变性或微观相互作用的特殊实现如何，这个结论都是成立的：我们因此称之为“超宇宙”。“反常的输运行为归因于长寿命的巨准粒子被热涨落装扮。我们提供了一个代数的观点，相应的敷料变换和阐明正式连接到融合身份之间的量子群字符。我们确定巨准粒子与非线性孤子模式的经典场论，描述低能量激发以上铁磁真空。我们对这些场论的分析还提供了低能的完整分类（即，量子各向同性铁磁链的Goldstone模）谱。
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.