{"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/classification-of-symmetry-enriched","title":"Classification of symmetry-enriched topological quantum spin liquids","arxiv_id":"2309.15118","date":"2023-09-26","proceeding":null,"authors":["Weicheng Ye","Liujun Zou"],"abstract":"We present a systematic framework to classify symmetry-enriched topological quantum spin liquids in two spatial dimensions. This framework can deal with all topological quantum spin liquids, which may be either Abelian or non-Abelian, chiral or non-chiral. It can systematically treat a general symmetry, which may include both lattice symmetry and internal symmetry, may contain anti-unitary symmetry, and may permute anyons. The framework applies to all types of lattices, and can systematically distinguish different lattice systems with the same symmetry group using their Lieb-Schultz-Mattis anomalies. We apply this framework to classify $U(1)_{2N}$ chiral states and non-Abelian Ising$^{(\\nu)}$ states enriched by a $p6\\times SO(3)$ or $p4\\times SO(3)$ symmetry, and $\\mathbb{Z}_N$ topological orders and $U(1)_{2N}\\times U(1)_{-2N}$ topological orders enriched by a $p6m\\times SO(3)\\times\\mathbb{Z}_2^T$, $p4m\\times SO(3)\\times\\mathbb{Z}_2^T$, $p6m\\times\\mathbb{Z}_2^T$ or $p4m\\times\\mathbb{Z}_2^T$ symmetry, where $p6$, $p4$, $p6m$ and $p4m$ are lattice symmetries, while $SO(3)$ and $\\mathbb{Z}_2^T$ are spin rotation and time reversal symmetries, respectively. In particular, we identify symmetry-enriched topological quantum spin liquids that are not easily captured by the usual parton-mean-field approach, including examples with the familiar $\\mathbb{Z}_2$ topological order.","url_abs":"https://arxiv.org/abs/2309.15118v3","url_pdf":"https://arxiv.org/pdf/2309.15118v3.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":"classification-of-symmetry-enriched","repo_url":"https://github.com/weicheng-ye/classification-of-qsl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}