The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz
We show that the Lipkin-Meshkov-Glick 2𝑁-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 𝑟-matrix and to an external magnetic field directed along one axis. We propose an exactly-solvab...
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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| Summary: | We show that the Lipkin-Meshkov-Glick 2𝑁-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 𝑟-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 𝑟-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 𝑁 = 1, 2.
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| ISSN: | 1815-0659 |