A unique feature of non-Hermitian systems is the extreme sensitivity of the eigenspectrum to boundary conditions with the emergence of the non-Hermitian skin effect (NHSE). A NHSE originates from the point-gap topology of complex eigenspectrum, where an extensive number of eigen-states are anomalously localized at the boundary driven by nonreciprocal dissipation. Two different approaches to create localization are disorder and flat-band spectrum, and their interplay can lead to the anomalous inverse Anderson localization, where the Bernoulli anti-symmetric disorder induces mobility in a full-flat band system in the presence of Aharonov–Bohm (AB) Cage. In this work, we study the localization–delocalization transitions due to the interplay of the point-gap topology, flat band and correlated disorder in the one-dimensional rhombic lattice, where both its Hermitian and non-Hermitian structures show AB cage in the presence of magnetic flux. Although it remains the coexistence of localization and delocalization for the Hermitian rhombic lattice in the presence of the random anti-symmetric disorder, it surprisingly becomes complete delocalization, accompanied by the emergence of NHSE. To further study the effects from the Bernoulli anti-symmetric disorder, we found the similar NHSE due to the interplay of the point-gap topology, correlated disorder and flat bands. Our anomalous localization–delocalization property can be experimentally tested in the classical physical platform, such as electrical circuit.

非厄米系统的一个独特特征是随着非厄米集肤效应（NHSE）的出现，本征谱对边界条件极其敏感。 NHSE 起源于复杂本征谱的点隙拓扑，其中大量本征态异常局域于由不可逆耗散驱动的边界处。创建局域化的两种不同方法是无序和平带频谱，它们的相互作用可能导致异常逆安德森局域化，其中伯努利反对称无序在阿哈罗诺夫-玻姆存在的情况下在全平带系统中引起移动性（ AB) 笼子。在这项工作中，我们研究了由于一维菱形晶格中点隙拓扑、平带和相关无序的相互作用而引起的局域-离域转变，其中其厄米特和非厄米特结构都显示出AB笼的存在磁通量。尽管在随机反对称无序存在的情况下，埃尔米特菱形晶格仍然保持局域化和离域化共存，但令人惊讶的是，它变得完全离域化，并伴随着NHSE的出现。为了进一步研究伯努利反对称无序的影响，由于点隙拓扑、相关无序和平带的相互作用，我们发现了类似的 NHSE。我们的异常定位-离域特性可以在经典物理平台（例如电路）中进行实验测试。