The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy
Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master T-operator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It s...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2014 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146851 |
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| Cite this: | The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy / A. Zabrodin // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 42 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862533823250563072 |
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| author | Zabrodin, A. |
| author_facet | Zabrodin, A. |
| citation_txt | The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy / A. Zabrodin // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 42 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master T-operator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars-Schneider system of particles.
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| first_indexed | 2025-11-24T06:30:46Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146851 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T06:30:46Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zabrodin, A. 2019-02-11T17:12:22Z 2019-02-11T17:12:22Z 2014 The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy / A. Zabrodin // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 42 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 81Q80; 05E05 DOI:10.3842/SIGMA.2014.006 https://nasplib.isofts.kiev.ua/handle/123456789/146851 Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master T-operator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars-Schneider system of particles. This paper is a contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa. The full
 collection is available at http://www.emis.de/journals/SIGMA/InfiniteAnalysis2013.html.
 The author thanks A. Alexandrov, A. Gorsky, V. Kazakov, S. Khoroshkin, I. Krichever, S. Leurent,
 M. Olshanetsky, A. Orlov, T. Takebe, Z. Tsuboi, and A. Zotov for discussions. Referees’
 remarks which helped to improve the manuscript are gratefully acknowledged. This work was
 supported in part by RFBR grant 11-02-01220, by joint RFBR grants 12-02-91052-CNRS, 12-
 02-92108-JSPS and by Ministry of Science and Education of Russian Federation under contract
 8207 and by grant NSh-3349.2012.2 for support of leading scientific schools. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy Article published earlier |
| spellingShingle | The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy Zabrodin, A. |
| title | The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy |
| title_full | The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy |
| title_fullStr | The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy |
| title_full_unstemmed | The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy |
| title_short | The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy |
| title_sort | master t-operator for inhomogeneous xxx spin chain and mkp hierarchy |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146851 |
| work_keys_str_mv | AT zabrodina themastertoperatorforinhomogeneousxxxspinchainandmkphierarchy AT zabrodina mastertoperatorforinhomogeneousxxxspinchainandmkphierarchy |