Scaling rule for the critical non-Hermitian skin effect
Scaling rule for the critical non-Hermitian skin effect
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DOI：
10.1103/physrevb.104.165117
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发表时间：
2021-07
影响因子：
3.7
通讯作者：
Kazuki Yokomizo;S. Murakami
中科院分区：
文献类型：
--
作者：
Kazuki Yokomizo;S. Murakami
非厄米系统表现出非厄米趋肤效应，其中体态在具有开边界条件的系统的边界处被局域化。本文研究了具有临界非厄米趋肤效应的特定非厄米模型中本征态的局域化长度对系统尺寸的依赖性，其中能谱在热力学极限下经历不连续跃迁.我们分析表明，本征态表现出显着的本地化，称为无标度本地化，本地化长度是成比例的系统大小。我们的结果为无标度局域化提供了理论支持，而在以前的工作中，无标度局域化仅在数值上被提出。
Non-Hermitian systems show a non-Hermitian skin effect, where the bulk states are localized at a boundary of the systems with open boundary conditions. In this paper, we study dependence of the localization length of the eigenstates on a system size in a specific non-Hermitian model with a critical non-Hermitian skin effect, where the energy spectrum undergoes discontinuous transition in the thermodynamic limit. We analytically show that the eigenstates exhibit remarkable localization, known as scale-free localization, where the localization length is proportional to a system size. Our result gives a theoretical support for the scale-free localization, which has been proposed only numerically in previous works.