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SIGMA, 2017, Volume 13, 094, 13 pages (Mi sigma1294)  

This article is cited in 4 scientific papers (total in 4 papers)

Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary

Nicolas Crampe

Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, Montpellier, France

Abstract: We solve the XXZ Gaudin model with generic boundary using the modified algebraic Bethe ansatz. The diagonal and triangular cases have been recovered in this general framework. We show that the model for odd or even lengths has two different behaviors. The corresponding Bethe equations are computed for all the cases. For the chain with even length, inhomogeneous Bethe equations are necessary. The higher spin Gaudin models with generic boundary is also treated.

Keywords: integrability; algebraic Bethe ansatz; Gaudin models; Bethe equations.

DOI: https://doi.org/10.3842/SIGMA.2017.094

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Bibliographic databases:

MSC: 81R12; 17B80; 37J35
Received: November 1, 2017; in final form December 6, 2017; Published online December 13, 2017
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Citation: Nicolas Crampe, “Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary”, SIGMA, 13 (2017), 094, 13 pp.

Citation in format AMSBIB
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\by Nicolas~Crampe
\paper Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary
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\papernumber 094
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. C. Dimo, A. Faribault, “Quadratic operator relations and Bethe equations for spin-1/2 Richardson-Gaudin models”, J. Phys. A-Math. Theor., 51:32 (2018), 325202  crossref  isi
    2. N. A. Slavnov, S. Belliard, B. Vallet, “Modified Algebraic Bethe Ansatz: Twisted XXX Case”, SIGMA, 14 (2018), 054, 18 pp.  mathnet  crossref
    3. N. Crampe, I R. Nepomechie, “Equivalent T-Q relations and exact results for the open TASEP”, J. Stat. Mech.-Theory Exp., 2018, 103105  crossref  isi  scopus
    4. Salom I., Manojlovic N., Cirilo Antonio N., “Generalized Sl (2) Gaudin Algebra and Corresponding Knizhnik-Zamolodchikov Equation”, Nucl. Phys. B, 939 (2019), 358–371  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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