Scale-Free Response with Directional Amplification in Critical Non-Hermitian Systems

Quantum Physics [Submitted on 21 Apr 2026] Scale-Free Response with Directional Amplification in Critical Non-Hermitian Systems Kunling Zhou, Zihe Yang, Bowen Zeng, Yong Hu The non-Hermitian skin effect can lead to directional amplification of response, with the associated end-to-end Green's function generally exhibiting size dependence. Any deviation in length or local disorder can drastically alter the amplification factor, rendering the response fragile in practical implementations. In this work, we identify a new type of scale-free, topological, and directionally amplified response in a Hatano-Nelson model under perturbed open boundary conditions. The scale-free response can be attributed to the first order boundary effect and characterized by a winding number defined on a continuous generalization of the finite-size Brillouin zone-a concept introduced in this work. Such scale-free behavior endows the end-to-end Green's function with significant robustness and making it promising for practical applications. Comments: 5 pages, 3 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.18990 [quant-ph]   (or arXiv:2604.18990v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.18990 Focus to learn more Submission history From: Bowen Zeng [view email] [v1] Tue, 21 Apr 2026 02:22:53 UTC (1,397 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)