非阿贝尔量子链中非遍历相的微扰不稳定性
Perturbative instability of non-ergodic phases in non-Abelian quantum chains
摘要：
多体量子动力学领域的一个重要挑战是确定物质在多体局域化（MBL）之外的非遍历态。具有非阿贝尔对称性的强无序自旋链和非阿贝尔任意子链是自然的候选者，因为它们与标准MBL不相容。在这样的链中，实空间重整化群方法预测了一个部分局域化的、非遍历的区域，称为量子临界玻璃（MBL的临界变体）。这种机制的特点是运动积分和对称本征态的树状层次结构，具有纠缠熵，其尺度为几何增强面积定律。我们认为，这种试探性的非遍历状态是微扰不稳定的非对角矩阵元素的缩放和访问的本地扰动的水平间距的分析计算。我们的结果表明，具有非阿贝尔对称性的强无序链在长时间内表现出自发对称性破缺或遍历热行为。我们确定相关的长度和时间尺度热化：即使这样的链最终热化，他们可以表现出非遍历动力学参数长的时间尺度与非解析依赖于无序强度。
英文摘要：
An important challenge in the field of many-body quantum dynamics is to identify non-ergodic states of matter beyond many-body localization (MBL). Strongly disordered spin chains with non-Abelian symmetry and chains of non-Abelian anyons are natural candidates, as they are incompatible with standard MBL. In such chains, real space renormalization group methods predict a partially localized, non-ergodic regime known as a quantum critical glass (a critical variant of MBL). This regime features a tree-like hierarchy of integrals of motion and symmetric eigenstates with entanglement entropy that scales as a logarithmically enhanced area law. We argue that such tentative non-ergodic states are perturbatively unstable using an analytic computation of the scaling of off-diagonal matrix elements and accessible level spacing of local perturbations. Our results indicate that strongly disordered chains with non-Abelian symmetry display either spontaneous symmetry breaking or ergodic thermal behavior at long times. We identify the relevant length and time scales for thermalization: even if such chains eventually thermalize, they can exhibit non-ergodic dynamics up to parametrically long time scales with a non-analytic dependence on disorder strength.
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