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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2014
1. Verfasser: Zabrodin, A.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2014
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146851
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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
id nasplib_isofts_kiev_ua-123456789-146851
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy
spellingShingle The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy
Zabrodin, A.
title_short 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_sort master t-operator for inhomogeneous xxx spin chain and mkp hierarchy
author Zabrodin, A.
author_facet Zabrodin, A.
publishDate 2014
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/146851
fulltext
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.
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