Vertex Models and Spin Chains in Formulas and Pictures
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are introduced. Their explicit analytical forms for the case of integra...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210227 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Vertex Models and Spin Chains in Formulas and Pictures / K.S. Nirov, A.V. Razumov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 77 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862560213062647808 |
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| author | Nirov, K.S. Razumov, A.V. |
| author_facet | Nirov, K.S. Razumov, A.V. |
| citation_txt | Vertex Models and Spin Chains in Formulas and Pictures / K.S. Nirov, A.V. Razumov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 77 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are introduced. Their explicit analytical forms for the case of integrable systems associated with the quantum loop algebra Uq(L(slₗ₊₁)) are given. The commutativity conditions for the transfer operators of lattices with a boundary are derived by the graphical method. Our consideration reveals useful advantages of the graphical approach for certain problems in the theory of quantum integrable systems.
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| first_indexed | 2025-12-07T21:24:50Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210227 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:50Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Nirov, K.S. Razumov, A.V. 2025-12-04T13:02:47Z 2019 Vertex Models and Spin Chains in Formulas and Pictures / K.S. Nirov, A.V. Razumov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 77 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B37; 17B80; 16T05; 16T25 arXiv: 1811.09401 https://nasplib.isofts.kiev.ua/handle/123456789/210227 https://doi.org/10.3842/SIGMA.2019.068 We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are introduced. Their explicit analytical forms for the case of integrable systems associated with the quantum loop algebra Uq(L(slₗ₊₁)) are given. The commutativity conditions for the transfer operators of lattices with a boundary are derived by the graphical method. Our consideration reveals useful advantages of the graphical approach for certain problems in the theory of quantum integrable systems. This work was supported in part by the Russian Foundation for Basic Research grant # 16-01-00473. KhSN was also supported by the DFG grant # BO3401/31 and by the Russian Academic Excellence Project ‘5-100’; results obtained in Section 3 were funded by the HSE Faculty of Mathematics. We thank our colleagues and coauthors H. Boos, F. Göhmann, and A. Klümper for numerous fruitful discussions. AVR thanks the Max Planck Institute for Mathematics in Bonn, where this work was finished, for the warm hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Vertex Models and Spin Chains in Formulas and Pictures Article published earlier |
| spellingShingle | Vertex Models and Spin Chains in Formulas and Pictures Nirov, K.S. Razumov, A.V. |
| title | Vertex Models and Spin Chains in Formulas and Pictures |
| title_full | Vertex Models and Spin Chains in Formulas and Pictures |
| title_fullStr | Vertex Models and Spin Chains in Formulas and Pictures |
| title_full_unstemmed | Vertex Models and Spin Chains in Formulas and Pictures |
| title_short | Vertex Models and Spin Chains in Formulas and Pictures |
| title_sort | vertex models and spin chains in formulas and pictures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210227 |
| work_keys_str_mv | AT nirovks vertexmodelsandspinchainsinformulasandpictures AT razumovav vertexmodelsandspinchainsinformulasandpictures |