Perturbative instability of nonergodic phases in non-Abelian quantum chains
Perturbative instability of nonergodic phases in non-Abelian quantum chains
复制标题
非阿贝尔量子链中非遍历相的微扰不稳定性
作者：
Brayden Ware;D. Abanin;R. Vasseur
多体量子动力学领域的一个重要挑战是识别多体局部化（MBL）之外的物质的非遍历态。具有非阿贝尔对称的强无序自旋链和非阿贝尔任意子链是自然的候选，因为它们与标准MBL不相容。在这样的链中，实空间重整群方法预测了一个局部的、非遍历的状态，称为量子临界玻璃（MBL的一个关键变体）。这种制度的特点是运动积分和对称特征态的树状层次结构，具有纠缠熵，其尺度为对数增强的面积律。我们利用非对角矩阵元素的尺度解析计算和局部扰动的可达水平间距，论证了这种暂定非遍历状态是微扰不稳定的。我们的研究结果表明，具有非阿贝尔对称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。我们确定了热化的相关长度和时间尺度：即使这些链最终热化，它们也可以表现出非遍历动力学，直至参数化长时间尺度，对无序强度具有非解析性依赖。
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.
影响因子：
3.7
作者：
Friedman, Aaron J.;Vasseur, Romain;Parameswaran, S. A.
通讯作者：
Parameswaran, S. A.
影响因子：
3.7
作者：
Gopalakrishnan, Sarang;Huse, David A.
通讯作者：
Huse, David A.
影响因子：
56.9
作者：
Lukin, Alexander;Rispoli, Matthew;Greiner, Markus
通讯作者：
Greiner, Markus