连接两类非厄米性：利用Lanczos变换从非互易耦合到虚势

中文摘要 AI 辅助

物理系统中发现的两种非厄米性类型，即非互易耦合和复势，近年来引起了相当大的兴趣。前者导致非厄米趋肤效应，而后者则引发一系列非厄米对称性，如宇称-时间（$PT$）对称和粒子-空穴对称。尽管这两种非厄米形式已被纳入同一模型中，但迄今为止它们被视为不同的非厄米性家族。在本工作中，我们利用Lanczos变换在它们之间建立了等谱映射。更具体地说，我们证明了一个具有非互易和空间变化耦合的广义Hatano-Nelson模型$H$可以映射到一个具有实对称耦合和虚在位势的紧束缚模型$H_L$。即使原始$H$已经具有虚势和奇异点，这一结果也成立。我们的工作提供了对不同形式非厄米性之间联系的重新理解。它还提供了一种方法，以获得对$H_L$中在$H$中难以捉摸的奇异点的直观物理理解。最后，我们的发现还保证了一种构建具有复势和实谱的非厄米系统的通用方法，而无需$PT$对称性。

英文摘要

Two types of non-Hermiticity found in physical systems, i.e., non-reciprocal couplings and complex potentials, have gained considerable interest recently. The former leads to the non-Hermitian skin effect, while the latter gives rise to a range of non-Hermitian symmetries such as parity-time ($PT$) and particle-hole symmetries. Although these two non-Hermitian forms have been incorporated in the same models, so far they have been treated as distinct families of non-Hermiticity. In this work, we establish an isospectral mapping between them using the Lanczos transformation. More specifically, we show that a generalized Hatano-Nelson model $H$ with non-reciprocal and spatially varying couplings can be mapped to a tight-binding model $H_L$ with real symmetric couplings and an imaginary on-site potential. This result holds even when the original $H$ already has an imaginary potential and exceptional points. Our work provides a refreshed understanding of the connection between different forms of non-Hermiticity. It also offers an approach to obtaining an intuitive physical understanding of exceptional points in $H_L$ that are elusive in $H$. Finally, our findings also warrant a versatile approach to constructing non-Hermitian systems with a complex potential and a real spectrum, without $PT$ symmetry.

发表机构

• Department of Physics and Astronomy, College of Staten Island, CUNY（纽约市立学院斯塔滕岛分校物理与天文系）
• The Graduate Center, CUNY（纽约市立大学研究生院）

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6 pages, 5 figures