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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | https://arxiv.org/abs/2310.03816 |
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| _version_ | 1866917841439031296 |
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| author | Hietarinta, Jarmo Martin, Paul Rowell, Eric C. |
| author_facet | Hietarinta, Jarmo Martin, Paul Rowell, Eric C. |
| contents | We find all solutions to the constant Yang--Baxter equation $R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}$ in three dimensions, subject to an additive charge-conservation ansatz. This ansatz is a generalisation of (strict) charge-conservation, for which a complete classification in all dimensions was recently obtained. Additive charge-conservation introduces additional sector-coupling parameters -- in 3 dimensions there are $4$ such parameters. In the generic dimension 3 case, in which all of the $4$ parameters are nonzero, we find there is a single 3 parameter family of solutions. We give a complete analysis of this solution, giving the structure of the centraliser (symmetry) algebra in all orders. We also solve the remaining cases with three, two, or one nonzero sector-coupling parameter(s). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03816 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solutions to the constant Yang-Baxter equation: additive charge conservation in three dimensions Hietarinta, Jarmo Martin, Paul Rowell, Eric C. Quantum Algebra Statistical Mechanics High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems We find all solutions to the constant Yang--Baxter equation $R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}$ in three dimensions, subject to an additive charge-conservation ansatz. This ansatz is a generalisation of (strict) charge-conservation, for which a complete classification in all dimensions was recently obtained. Additive charge-conservation introduces additional sector-coupling parameters -- in 3 dimensions there are $4$ such parameters. In the generic dimension 3 case, in which all of the $4$ parameters are nonzero, we find there is a single 3 parameter family of solutions. We give a complete analysis of this solution, giving the structure of the centraliser (symmetry) algebra in all orders. We also solve the remaining cases with three, two, or one nonzero sector-coupling parameter(s). |
| title | Solutions to the constant Yang-Baxter equation: additive charge conservation in three dimensions |
| topic | Quantum Algebra Statistical Mechanics High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2310.03816 |