{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/unsupervised-learning-of-topological-non","title":"Unsupervised Learning of Topological Non-Abelian Braiding in Non-Hermitian Bands","arxiv_id":"2401.17968","date":"2024-01-31","proceeding":null,"authors":["Yang Long","Haoran Xue","Baile Zhang"],"abstract":"The topological classification of energy bands has laid the groundwork for the discovery of various topological phases of matter in recent decades. While this classification has traditionally focused on real-energy bands, recent studies have revealed the intriguing topology of complex-energy, or non-Hermitian bands. For example, the spectral winding of complex-energy bands can from unique topological structures like braids, holding promise for advancing quantum computing. However, discussions of complex-energy braids have been largely limited to the Abelian braid group $\\mathbb{B}_2$ for its relative simplicity, while identifying topological non-Abelian braiding is still difficult since it has no universal topological invariant for characterization. Here, we present a machine learning algorithm for the unsupervised identification of non-Abelian braiding of multiple complex-energy bands. The consistency with Artin's well-known topological equivalence conditions in braiding is demonstrated. Inspired by the results from unsupervised learning, we also introduce a winding matrix as a topological invariant in charactering the braiding topology and unveiling the bulk-edge correspondence of non-Abelian braided non-Hermitian bands. Finally, we extend our approach to identify non-Abelian braiding topology in 2D/3D exceptional semimetals and successfully address the unknotting problem in an unsupervised manner.","url_abs":"https://arxiv.org/abs/2401.17968v1","url_pdf":"https://arxiv.org/pdf/2401.17968v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"unsupervised-learning-of-topological-non","repo_url":"https://github.com/longyangking/ml_topology_non_Abelian_braiding","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}