Anatomy of topological Anderson transitions
Anatomy of topological Anderson transitions
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DOI：
10.1103/physrevb.108.224201
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发表时间：
2023-01
影响因子：
3.7
通讯作者：
Hao-Kai Zhang;A. Kamenev
中科院分区：
文献类型：
--
作者：
Hao-Kai Zhang;A. Kamenev
我们研究了拓扑无序链中拓扑Anderson跃迁的介观特征。为此，我们引入了有限大小系统中拓扑指数的整数值样本特定定义。它的相图显示出一种令人着迷的间歇性拓扑相结构，称为拓扑岛。它们的存在植根于基本随机多项式的实零点。他们的统计数据显示了有限大小的标度，指向了体拓扑Anderson相变的位置。虽然AIII和BDI对称类的平均理论相当相似，但对应的拓扑岛模式及其统计性质是不同的。我们还讨论了介观系统中尖锐的拓扑跃迁的可观测特征，如持续电流和纠缠光谱。
We study mesoscopic signatures of the topological Anderson transitions in topological disordered chains. To this end we introduce an integer-valued sample-specific definition of the topological index in finite size systems. Its phase diagram exhibits a fascinating structure of intermittent topological phases, dubbed topological islands. Their existence is rooted in the real zeros of the underlying random polynomial. Their statistics exhibits finite-size scaling, pointing to the location of the bulk topological Anderson transition. While the average theories in AIII and BDI symmetry classes are rather similar, the corresponding patterns of topological islands and their statistics are qualitatively different. We also discuss observable signatures of sharp topological transitions in mesoscopic systems, such as persistent currents and entanglement spectra.