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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210703 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | New Separation of Variables for the Classical XXX and XXZ Heisenberg Spin Chains. Guido Magnano and Taras Skrypnyk. SIGMA 16 (2020), 047, 27 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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| ISSN: | 1815-0659 |