Mechanism for scale-free skin effect in one-dimensional systems

[2604.01638] Mechanism for scale-free skin effect in one-dimensional systems Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2604.01638 (quant-ph) [Submitted on 2 Apr 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Mechanism for scale-free skin effect in one-dimensional systems Authors: Shu-Xuan Wang , Zhongbo Yan View PDF HTML (experimental) Abstract: Non-Hermitian skin effect is one of the most captivating phenomena in non-Hermitian systems, characterized by the extensive localization of eigenstates near open boundaries. In its conventional form, the localization length of a skin mode is independent of the system size. Remarkably, however, when the open boundaries are coupled to realize a generalized boundary condition, the localization length can undergo a drastic transformation, becoming proportional to the system length. This intriguing regime is known as the scale-free skin effect (SFSE). Although SFSE has been observed in numerous one-dimensional non-Hermitian models through case-by-case studies, a unified theoret ical framework capable of predicting its emergence and characteristic properties remains absent. In this work, we take a firm step forward by establishing a model-independent framework for the ana lytic determination of scale-free localization lengths in certain regimes. Our key insight is to treat generalized boundary conditions as a perturbation of the periodic boundary conditions, thereby circumventing the singular response-to-perturbation that would otherwise arise if they were pertur batively treated relative to open boundary conditions. Our work sheds new light on understanding SFSE in non-Hermitian systems. Comments: 9 pages, 2 figures Subjects: Quantum Physics (quant-ph) ; Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Cite as: arXiv:2604.01638 [quant-ph] (or arXiv:2604.01638v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.01638 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Shu-Xuan Wang [ view email ] [v1] Thu, 2 Apr 2026 05:25:58 UTC (469 KB) [v2] Fri, 28 Aug 2026 05:36:22 UTC (472 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.mes-hall References & Citations INSPIRE HEP SciX 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

Related documents

• Mechanism for scale-free skin effect in one-dimensional systems#682632
• Assessment of a Skin Barrier#912051
• On the illumination of centrally symmetric cap bodies in small dimensions#183104
• On the illumination of centrally symmetric cap bodies in small dimensions#183054
• On the illumination of centrally symmetric cap bodies in small dimensions#183004