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SIGMA, 2011, Volume 7, 012, 22 pages (Mi sigma570)  

This article is cited in 17 scientific papers (total in 17 papers)

Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End

Ghali Filalia, Nikolai Kitanineb

a Université de Cergy-Pontoise, LPTM UMR 8089 du CNRS, 2 av. Adolphe Chauvin, 95302 Cergy-Pontoise, France
b Université de Bourgogne, Institut de Mathématiques de Bourgogne UMR 5584 du CNRS, 9 av. Alain Savary – B.P. 47 870, 21078 Dijon, France

Abstract: In this paper we consider two a priori very different problems: construction of the eigenstates of the spin chains with non parallel boundary magnetic fields and computation of the partition function for the trigonometric solid-on-solid (SOS) model with one reflecting end and domain wall boundary conditions. We show that these two problems are related through a gauge transformation (so-called vertex-face transformation) and can be solved using the same dynamical reflection algebras.

Keywords: algebraic Bethe ansatz; spin chains; dynamical reflection algebra; SOS models

DOI: https://doi.org/10.3842/SIGMA.2011.012

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Full text: http://emis.mi.ras.ru/journals/SIGMA/2011/012/
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ArXiv: 1011.0660
MSC: 82B20; 82B23
Received: October 28, 2010; in final form January 11, 2011; Published online January 27, 2011
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Citation: Ghali Filali, Nikolai Kitanine, “Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End”, SIGMA, 7 (2011), 012, 22 pp.

Citation in format AMSBIB
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\by Ghali Filali, Nikolai Kitanine
\paper Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End
\jour SIGMA
\yr 2011
\vol 7
\papernumber 012
\totalpages 22
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\crossref{https://doi.org/10.3842/SIGMA.2011.012}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yang W.-L., Chen X., Feng J., Hao K., Wu K., Yang Zh.-Y., Zhang Ya.-Zh., “Scalar products of the open XYZ chain with non-diagonal boundary terms”, Nuclear Phys B, 848:3 (2011), 523–544  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Niccoli G., “Completeness of Bethe ansatz by Sklyanin SOV for cyclic representations of integrable quantum models”, Journal of High Energy Physics, 2011, no. 3, 123  crossref  mathscinet  zmath  isi  scopus
    3. Murgan R., “A note on the IR limit of the NLIEs of boundary supersymmetric sine-Gordon model”, Journal of High Energy Physics, 2011, no. 9, 059  crossref  mathscinet  zmath  isi  scopus
    4. Filali G., “Elliptic dynamical reflection algebra and partition function of SOS model with reflecting end”, J Geom Phys, 61:10 (2011), 1789–1796  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Galleas W., “Multiple integral representation for the trigonometric SOS model with domain wall boundaries”, Nuclear Phys B, 858:1 (2012), 117–141  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Chen Xi, Feng Jun, Hao Kun, Wu Ke, Yang Wen-Li, Yang Zhan-Ying, Zhang Yao-Zhong, “Drinfeld Twist and Symmetric Bethe Vectors of Open XYZ Chain with Non-Diagonal Boundary Terms”, Commun Theor Phys (Beijing), 57:1 (2012), 19–28  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Faldella S., Niccoli G., “Sov Approach for Integrable Quantum Models Associated with General Representations on Spin-1/2 Chains of the 8-Vertex Reflection Algebra”, J. Phys. A-Math. Theor., 47:11 (2014), 115202  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    8. Kitanine N. Maillet J.M. Niccoli G., “Open Spin Chains with Generic Integrable Boundaries: Baxter Equation and Bethe Ansatz Completeness From Separation of Variables”, J. Stat. Mech.-Theory Exp., 2014, P05015  crossref  mathscinet  isi  scopus
    9. Faldella S., Kitanine N., Niccoli G., “The Complete Spectrum and Scalar Products For the Open Spin-1/2 Xxz Quantum Chains With Non-Diagonal Boundary Terms”, J. Stat. Mech.-Theory Exp., 2014, P01011  crossref  mathscinet  isi  elib  scopus
    10. Belliard S. Pimenta R.A., “Modified Algebraic Bethe Ansatz For Xxz Chain on the Segment - II - General Cases”, Nucl. Phys. B, 894 (2015), 527–552  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Belliard S., “Modified Algebraic Bethe Ansatz For Xxz Chain on the Segment - i: Triangular Cases”, Nucl. Phys. B, 892 (2015), 1–20  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Stokman J.V., “Connection Problems For Quantum Affine Kz Equations and Integrable Lattice Models”, Commun. Math. Phys., 338:3 (2015), 1363–1409  crossref  zmath  adsnasa  isi  elib  scopus
    13. Stokman J., Vlaar B., “Koornwinder Polynomials and the Xxz Spin Chain”, J. Approx. Theory, 197:SI (2015), 69–100  crossref  mathscinet  zmath  isi  elib  scopus
    14. Reshetikhin, Nicolai; Stokman, Jasper; Vlaar, Bart, “Boundary Quantum Knizhnik–Zamolodchikov Equations and Bethe Vectors”, Commun. Math. Phys., 336:2 (2015), 953-986  crossref  mathscinet  zmath  scopus
    15. Kitanine N. Maillet J.M. Niccoli G. Terras V., “The Open Xxx Spin Chain in the Sov Framework: Scalar Product of Separate States”, J. Phys. A-Math. Theor., 50:22 (2017), 224001  crossref  mathscinet  zmath  isi  scopus
    16. Baseilhac P., Martin X., “A Bispectral Q-Hypergeometric Basis For a Class of Quantum Integrable Models”, J. Math. Phys., 59:1 (2018), 011704  crossref  mathscinet  zmath  isi  scopus
    17. Kitanine N. Maillet J.M. Niccoli G. Terras V., “The Open Xxz Spin Chain in the Sov Framework: Scalar Product of Separate States”, J. Phys. A-Math. Theor., 51:48 (2018), 485201  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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