Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain
We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case. We review the multiple-integral representations of correlation functions...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147175 |
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| Cite this: | Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain / T. Deguchi, J. Sato // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 73 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862709495662116864 |
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| author | Deguchi, T. Sato, J. |
| author_facet | Deguchi, T. Sato, J. |
| citation_txt | Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain / T. Deguchi, J. Sato // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 73 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case. We review the multiple-integral representations of correlation functions for the integrable higher-spin XXZ chains derived in a region of the massless regime including the anti-ferromagnetic point. Here we make use of the gauge transformations between the symmetric and asymmetric R-matrices, which correspond to the principal and homogeneous gradings, respectively, and we send the inhomogeneous parameters to the set of complete 2s-strings. We also give a numerical support for the analytical expression of the one-point functions in the spin-1 case.
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| first_indexed | 2025-12-07T17:18:07Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147175 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:18:07Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Deguchi, T. Sato, J. 2019-02-13T18:12:08Z 2019-02-13T18:12:08Z 2011 Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain / T. Deguchi, J. Sato // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 73 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 82B23 DOI:10.3842/SIGMA.2011.056 https://nasplib.isofts.kiev.ua/handle/123456789/147175 We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case. We review the multiple-integral representations of correlation functions for the integrable higher-spin XXZ chains derived in a region of the massless regime including the anti-ferromagnetic point. Here we make use of the gauge transformations between the symmetric and asymmetric R-matrices, which correspond to the principal and homogeneous gradings, respectively, and we send the inhomogeneous parameters to the set of complete 2s-strings. We also give a numerical support for the analytical expression of the one-point functions in the spin-1 case. This paper is a contribution to the Proceedings of the International Workshop “Recent Advances in Quantum Integrable Systems”. The full collection is available at http://www.emis.de/journals/SIGMA/RAQIS2010.html.
 The authors would like to thank F. G¨ohmann, C. Matsui and K. Motegi for helpful comments. They are grateful for useful comments to many participants of the workshop RAQIS’10, June, 2010, LAPTH, Annecy, France. This work is partially supported by Grant-in-Aid for Scientific Research (C) No. 20540365. J. Sato is supported by Grant-in-Aid for JSPS fellows. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain Article published earlier |
| spellingShingle | Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain Deguchi, T. Sato, J. |
| title | Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain |
| title_full | Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain |
| title_fullStr | Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain |
| title_full_unstemmed | Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain |
| title_short | Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain |
| title_sort | quantum group uq(sl(2)) symmetry and explicit evaluation of the one-point functions of the integrable spin-1 xxz chain |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147175 |
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