New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains
We propose a non-standard separation of variables for the classical integrable XXX and XXZ spin chains with a degenerate twist matrix. We show that for the case of such twist matrices, one can interchange the role of classical separating functions A(u) and B(u) and construct a new full set of separa...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210703 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains. Guido Magnano and Taras Skrypnyk. SIGMA 16 (2020), 047, 27 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862711781777997824 |
|---|---|
| author | Magnano, Guido Skrypnyk, Taras |
| author_facet | Magnano, Guido Skrypnyk, Taras |
| citation_txt | New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains. Guido Magnano and Taras Skrypnyk. SIGMA 16 (2020), 047, 27 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We propose a non-standard separation of variables for the classical integrable XXX and XXZ spin chains with a degenerate twist matrix. We show that for the case of such twist matrices, one can interchange the role of classical separating functions A(u) and B(u) and construct a new full set of separated variables, satisfying simpler equations of separation and simpler Abel equations in comparison with the standard separated variables of Sklyanin. We show that for certain cases of the twist matrices, the constructed separated variables can be directly identified with action-angle coordinates.
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| first_indexed | 2025-12-17T12:04:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210703 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:32Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Magnano, Guido Skrypnyk, Taras 2025-12-15T15:24:58Z 2020 New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains. Guido Magnano and Taras Skrypnyk. SIGMA 16 (2020), 047, 27 pages 1815-0659 2020 Mathematics Subject Classification: 37J35; 17B80 arXiv:2006.01417 https://nasplib.isofts.kiev.ua/handle/123456789/210703 https://doi.org/10.3842/SIGMA.2020.047 We propose a non-standard separation of variables for the classical integrable XXX and XXZ spin chains with a degenerate twist matrix. We show that for the case of such twist matrices, one can interchange the role of classical separating functions A(u) and B(u) and construct a new full set of separated variables, satisfying simpler equations of separation and simpler Abel equations in comparison with the standard separated variables of Sklyanin. We show that for certain cases of the twist matrices, the constructed separated variables can be directly identified with action-angle coordinates. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains Article published earlier |
| spellingShingle | New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains Magnano, Guido Skrypnyk, Taras |
| title | New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains |
| title_full | New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains |
| title_fullStr | New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains |
| title_full_unstemmed | New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains |
| title_short | New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains |
| title_sort | new separation of variables for the classical xxx and xxz heisenberg spin chains |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210703 |
| work_keys_str_mv | AT magnanoguido newseparationofvariablesfortheclassicalxxxandxxzheisenbergspinchains AT skrypnyktaras newseparationofvariablesfortheclassicalxxxandxxzheisenbergspinchains |