Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain
We consider the XXX spin-1/2 Heisenberg chain on the circle with an arbitrary twist. We characterize its spectral problem using the modified algebraic Bethe anstaz and study the scalar product between the Bethe vector and its dual. We obtain modified Slavnov and Gaudin-Korepin formulas for the model...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147162 |
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| Cite this: | Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain / S. Belliard, R.A. Pimenta // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 37 назв. — англ. |
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Belliard, S. Pimenta, R.A. 2019-02-13T17:59:00Z 2019-02-13T17:59:00Z 2015 Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain / S. Belliard, R.A. Pimenta // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 37 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 82B23; 81R12 DOI:10.3842/SIGMA.2015.099 https://nasplib.isofts.kiev.ua/handle/123456789/147162 We consider the XXX spin-1/2 Heisenberg chain on the circle with an arbitrary twist. We characterize its spectral problem using the modified algebraic Bethe anstaz and study the scalar product between the Bethe vector and its dual. We obtain modified Slavnov and Gaudin-Korepin formulas for the model. Thus we provide a first example of such formulas for quantum integrable models without U(1) symmetry characterized by an inhomogenous Baxter T-Q equation. We thank J. Avan, N. Grosjean and R Nepomechie for discussions. R.A.P. would like to thanks the hospitality of the Laboratoire de Physique Th´eorique et Mod´elisation at the Universit´e de Cergy-Pontoise where a part of this work was done. S.B. is supported by the Universit´e de Cergy-Pontoise post doctoral fellowship. R.A.P. is supported by Sao Paulo Research Foundation (FAPESP), grants # 2014/00453-8 and # 2014/20364-0. We also thank the referees for their constructive remarks. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain |
| spellingShingle |
Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain Belliard, S. Pimenta, R.A. |
| title_short |
Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain |
| title_full |
Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain |
| title_fullStr |
Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain |
| title_full_unstemmed |
Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain |
| title_sort |
slavnov and gaudin-korepin formulas for models without u(1) symmetry: the twisted xxx chain |
| author |
Belliard, S. Pimenta, R.A. |
| author_facet |
Belliard, S. Pimenta, R.A. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We consider the XXX spin-1/2 Heisenberg chain on the circle with an arbitrary twist. We characterize its spectral problem using the modified algebraic Bethe anstaz and study the scalar product between the Bethe vector and its dual. We obtain modified Slavnov and Gaudin-Korepin formulas for the model. Thus we provide a first example of such formulas for quantum integrable models without U(1) symmetry characterized by an inhomogenous Baxter T-Q equation.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147162 |
| citation_txt |
Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain / S. Belliard, R.A. Pimenta // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 37 назв. — англ. |
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| first_indexed |
2025-12-07T19:31:09Z |
| last_indexed |
2025-12-07T19:31:09Z |
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