{"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/revealing-the-phase-diagram-of-kitaev","title":"Revealing the Phase Diagram of Kitaev Materials by Machine Learning: Cooperation and Competition between Spin Liquids","arxiv_id":"2004.14415","date":"2020-04-29","proceeding":null,"authors":["Ke Liu","Nicolas Sadoune","Nihal Rao","Jonas Greitemann","Lode Pollet"],"abstract":"Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the honeycomb Kitaev-$\\Gamma$ model in a magnetic field. Our machine learns the global classical phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic $S_3$ magnets, and two modulated $S_3 \\times Z_3$ magnets. We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic order already occur in the large-$S$ limit, implying that critical parts of the physics of Kitaev materials can be understood at the classical level. Moreover, the two $S_3 \\times Z_3$ orders are induced by competition between Kitaev and $\\Gamma$ spin liquids and feature a different type of spin-lattice entangled modulation, which requires a matrix description instead of scalar phase factors. Our work provides a direct instance of a machine detecting new phases and paves the way towards the development of automated tools to explore unsolved problems in many-body physics.","url_abs":"https://arxiv.org/abs/2004.14415v4","url_pdf":"https://arxiv.org/pdf/2004.14415v4.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":"abstracts"},"code_links":[{"paper_slug":"revealing-the-phase-diagram-of-kitaev","repo_url":"https://gitlab.physik.uni-muenchen.de/tk-svm/tksvm-op","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"interpretable-machine-learning","task_name":"Interpretable Machine Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}