Nonabelian anyon condensation in 2+1d topological orders: A string-net model realization
Abstract We develop a comprehensive framework for realizing anyon condensation of topological orders within the string-net model by constructing a Hamiltonian that bridges the parent string-net model before and the child string-net model after anyon condensation. Our approach classifies all possible...
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SpringerOpen
2025-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2025)156 |
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| author | Yu Zhao Yidun Wan |
| author_facet | Yu Zhao Yidun Wan |
| author_sort | Yu Zhao |
| collection | DOAJ |
| description | Abstract We develop a comprehensive framework for realizing anyon condensation of topological orders within the string-net model by constructing a Hamiltonian that bridges the parent string-net model before and the child string-net model after anyon condensation. Our approach classifies all possible types of bosonic anyon condensation in any parent string-net model and identifies the basic degrees of freedom in the corresponding child models. The Kogut-Susskind lattice gauge theory model is a special case of our model if the full degrees of freedom of the model are truncated from SU(2) representations to quantum group SU(2) k . Compared with the traditional UMTC perspective of topological orders, our method offers a finer categorical description of anyon condensation at the microscopic level. We also explicitly represent relevant UMTC categorical entities characterizing anyon condensation through our model-based physical quantities, providing practical algorithms for calculating these categorical data. |
| format | Article |
| id | doaj-art-23ccde56178142efacc4eb9374c8f408 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-23ccde56178142efacc4eb9374c8f4082025-08-20T02:05:45ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025514410.1007/JHEP05(2025)156Nonabelian anyon condensation in 2+1d topological orders: A string-net model realizationYu Zhao0Yidun Wan1State Key Laboratory of Surface Physics, Center for Astronomy and Astrophysics, Department of Physics, Center for Field Theory and Particle Physics, and Institute for Nanoelectronic devices and Quantum Computing, Fudan UniversityState Key Laboratory of Surface Physics, Center for Astronomy and Astrophysics, Department of Physics, Center for Field Theory and Particle Physics, and Institute for Nanoelectronic devices and Quantum Computing, Fudan UniversityAbstract We develop a comprehensive framework for realizing anyon condensation of topological orders within the string-net model by constructing a Hamiltonian that bridges the parent string-net model before and the child string-net model after anyon condensation. Our approach classifies all possible types of bosonic anyon condensation in any parent string-net model and identifies the basic degrees of freedom in the corresponding child models. The Kogut-Susskind lattice gauge theory model is a special case of our model if the full degrees of freedom of the model are truncated from SU(2) representations to quantum group SU(2) k . Compared with the traditional UMTC perspective of topological orders, our method offers a finer categorical description of anyon condensation at the microscopic level. We also explicitly represent relevant UMTC categorical entities characterizing anyon condensation through our model-based physical quantities, providing practical algorithms for calculating these categorical data.https://doi.org/10.1007/JHEP05(2025)156AnyonsDuality in Gauge Field TheoriesPhase TransitionsTopological Field Theories |
| spellingShingle | Yu Zhao Yidun Wan Nonabelian anyon condensation in 2+1d topological orders: A string-net model realization Journal of High Energy Physics Anyons Duality in Gauge Field Theories Phase Transitions Topological Field Theories |
| title | Nonabelian anyon condensation in 2+1d topological orders: A string-net model realization |
| title_full | Nonabelian anyon condensation in 2+1d topological orders: A string-net model realization |
| title_fullStr | Nonabelian anyon condensation in 2+1d topological orders: A string-net model realization |
| title_full_unstemmed | Nonabelian anyon condensation in 2+1d topological orders: A string-net model realization |
| title_short | Nonabelian anyon condensation in 2+1d topological orders: A string-net model realization |
| title_sort | nonabelian anyon condensation in 2 1d topological orders a string net model realization |
| topic | Anyons Duality in Gauge Field Theories Phase Transitions Topological Field Theories |
| url | https://doi.org/10.1007/JHEP05(2025)156 |
| work_keys_str_mv | AT yuzhao nonabeliananyoncondensationin21dtopologicalordersastringnetmodelrealization AT yidunwan nonabeliananyoncondensationin21dtopologicalordersastringnetmodelrealization |