Integrability and braided tensor categories
Many integrable statistical mechanical models possess a fractional-spin conserved current. Such currents have been constructed by utilising quantum-group algebras and ideas from “discrete holomorphicity”. I find them naturally and much more generally using a braided tensor category, a topological st...
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| Fformat: | Journal article |
| Iaith: | English |
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Springer
2021
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| _version_ | 1826257169447649280 |
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| author | Fendley, P |
| author_facet | Fendley, P |
| author_sort | Fendley, P |
| collection | OXFORD |
| description | Many integrable statistical mechanical models possess a fractional-spin conserved current. Such currents have been constructed by utilising quantum-group algebras and ideas from “discrete holomorphicity”. I find them naturally and much more generally using a braided tensor category, a topological structure arising in knot invariants, anyons and conformal field theory. I derive a simple constraint on the Boltzmann weights admitting a conserved current, generalising one found using quantum-group algebras. The resulting trigonometric weights are typically those of a critical integrable lattice model, so the method here gives a linear way of “Baxterising”, i.e. building a solution of the Yang-Baxter equation out of topological data. It also illuminates why many models do not admit a solution. I discuss many examples in geometric and local models, including (perhaps) a new solution. |
| first_indexed | 2024-03-06T18:13:52Z |
| format | Journal article |
| id | oxford-uuid:03ee70e0-6824-4944-b34e-371da416c27a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:13:52Z |
| publishDate | 2021 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:03ee70e0-6824-4944-b34e-371da416c27a2022-03-26T08:49:15ZIntegrability and braided tensor categoriesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:03ee70e0-6824-4944-b34e-371da416c27aEnglishSymplectic ElementsSpringer2021Fendley, PMany integrable statistical mechanical models possess a fractional-spin conserved current. Such currents have been constructed by utilising quantum-group algebras and ideas from “discrete holomorphicity”. I find them naturally and much more generally using a braided tensor category, a topological structure arising in knot invariants, anyons and conformal field theory. I derive a simple constraint on the Boltzmann weights admitting a conserved current, generalising one found using quantum-group algebras. The resulting trigonometric weights are typically those of a critical integrable lattice model, so the method here gives a linear way of “Baxterising”, i.e. building a solution of the Yang-Baxter equation out of topological data. It also illuminates why many models do not admit a solution. I discuss many examples in geometric and local models, including (perhaps) a new solution. |
| spellingShingle | Fendley, P Integrability and braided tensor categories |
| title | Integrability and braided tensor categories |
| title_full | Integrability and braided tensor categories |
| title_fullStr | Integrability and braided tensor categories |
| title_full_unstemmed | Integrability and braided tensor categories |
| title_short | Integrability and braided tensor categories |
| title_sort | integrability and braided tensor categories |
| work_keys_str_mv | AT fendleyp integrabilityandbraidedtensorcategories |