The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz
We show that the Lipkin-Meshkov-Glick 2-fermion model is a particular case of a one-spin Gaudin-type model in an external magnetic field corresponding to a limiting case of a non-skew-symmetric elliptic -matrix and to an external magnetic field directed along one axis. We propose an exactly-solvable...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211714 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz. Taras Skrypnyk. SIGMA 18 (2022), 074, 18 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862551261264478208 |
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| author | Skrypnyk, Taras |
| author_facet | Skrypnyk, Taras |
| citation_txt | The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz. Taras Skrypnyk. SIGMA 18 (2022), 074, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show that the Lipkin-Meshkov-Glick 2-fermion model is a particular case of a one-spin Gaudin-type model in an external magnetic field corresponding to a limiting case of a non-skew-symmetric elliptic -matrix and to an external magnetic field directed along one axis. We propose an exactly-solvable generalization of the Lipkin-Meshkov-Glick fermion model based on the Gaudin-type model corresponding to the same -matrix but an arbitrary external magnetic field. This model coincides with the quantization of the classical Zhukovsky-Volterra gyrostat. We diagonalize the corresponding quantum Hamiltonian by means of the modified algebraic Bethe ansatz. We explicitly solve the corresponding Bethe-type equations for the case of small fermion number = 1, 2.
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| first_indexed | 2026-03-13T04:26:22Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211714 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T04:26:22Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Skrypnyk, Taras 2026-01-09T12:40:41Z 2022 The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz. Taras Skrypnyk. SIGMA 18 (2022), 074, 18 pages 1815-0659 2020 Mathematics Subject Classification: 81R12; 82B23; 17B80 arXiv:2210.04454 https://nasplib.isofts.kiev.ua/handle/123456789/211714 https://doi.org/10.3842/SIGMA.2022.074 We show that the Lipkin-Meshkov-Glick 2-fermion model is a particular case of a one-spin Gaudin-type model in an external magnetic field corresponding to a limiting case of a non-skew-symmetric elliptic -matrix and to an external magnetic field directed along one axis. We propose an exactly-solvable generalization of the Lipkin-Meshkov-Glick fermion model based on the Gaudin-type model corresponding to the same -matrix but an arbitrary external magnetic field. This model coincides with the quantization of the classical Zhukovsky-Volterra gyrostat. We diagonalize the corresponding quantum Hamiltonian by means of the modified algebraic Bethe ansatz. We explicitly solve the corresponding Bethe-type equations for the case of small fermion number = 1, 2. The author is grateful to N. Manojlovic for the Bethe ansatz discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz Article published earlier |
| spellingShingle | The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz Skrypnyk, Taras |
| title | The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz |
| title_full | The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz |
| title_fullStr | The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz |
| title_full_unstemmed | The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz |
| title_short | The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz |
| title_sort | generalized lipkin-meshkov-glick model and the modified algebraic bethe ansatz |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211714 |
| work_keys_str_mv | AT skrypnyktaras thegeneralizedlipkinmeshkovglickmodelandthemodifiedalgebraicbetheansatz AT skrypnyktaras generalizedlipkinmeshkovglickmodelandthemodifiedalgebraicbetheansatz |