Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots
In this article, we study the thermodynamic limit of the form factors of the Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants of matrices that remain finite-dimensional in the thermodynamic...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211415 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots. Nikolai Kitanine and Giridhar Kulkarni. SIGMA 17 (2021), 112, 25 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862670602102374400 |
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| author | Kitanine, Nikolai Kulkarni, Giridhar |
| author_facet | Kitanine, Nikolai Kulkarni, Giridhar |
| citation_txt | Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots. Nikolai Kitanine and Giridhar Kulkarni. SIGMA 17 (2021), 112, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this article, we study the thermodynamic limit of the form factors of the Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants of matrices that remain finite-dimensional in the thermodynamic limit. We show how to treat all types of complex roots of the Bethe equations within this framework. In particular, we demonstrate that the Gaudin determinant for the higher-level Bethe equations arises naturally from the algebraic Bethe ansatz.
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| first_indexed | 2026-03-16T14:45:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211415 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T14:45:43Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kitanine, Nikolai Kulkarni, Giridhar 2026-01-02T08:27:53Z 2021 Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots. Nikolai Kitanine and Giridhar Kulkarni. SIGMA 17 (2021), 112, 25 pages 1815-0659 2020 Mathematics Subject Classification: 81U15; 81U40; 45F05 arXiv:2105.10244 https://nasplib.isofts.kiev.ua/handle/123456789/211415 https://doi.org/10.3842/SIGMA.2021.112 In this article, we study the thermodynamic limit of the form factors of the Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants of matrices that remain finite-dimensional in the thermodynamic limit. We show how to treat all types of complex roots of the Bethe equations within this framework. In particular, we demonstrate that the Gaudin determinant for the higher-level Bethe equations arises naturally from the algebraic Bethe ansatz. The work of N.K. was partially supported by the EIPHI Graduate School (contract ANR17-EURE-0002). N.K. would like to thank the LPTMS laboratory (Université Paris-Saclay) and the LPTHE laboratory (Sorbonne Université) for hospitality. The work of G.K. was supported by the Carnot Pasteur doctoral school of the UBFC. We would like to thank the referees for several useful comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots Article published earlier |
| spellingShingle | Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots Kitanine, Nikolai Kulkarni, Giridhar |
| title | Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots |
| title_full | Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots |
| title_fullStr | Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots |
| title_full_unstemmed | Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots |
| title_short | Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots |
| title_sort | form factors of the heisenberg spin chain in the thermodynamic limit: dealing with complex bethe roots |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211415 |
| work_keys_str_mv | AT kitaninenikolai formfactorsoftheheisenbergspinchaininthethermodynamiclimitdealingwithcomplexbetheroots AT kulkarnigiridhar formfactorsoftheheisenbergspinchaininthethermodynamiclimitdealingwithcomplexbetheroots |