L. V. Avdeev, A. A. Vladimirov, “Exceptional solutions to the Bethe ansatz equations”, TMF, 69:2 (1986), 163–174; Theoret. and Math. Phys., 69:2 (1986), 1071

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Teoreticheskaya i Matematicheskaya Fizika, 1986, Volume 69, Number 2, Pages 163–174 (Mi tmf5215)

This article is cited in 34 scientific papers (total in 34 papers)

Exceptional solutions to the Bethe ansatz equations

L. V. Avdeev, A. A. Vladimirov

Full-text PDF (1105 kB) Citations (34)

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Abstract: The properties of some special solutions of the equations of the Bethe ansatz are investigated. Examples of nontrivial Bethe vectors corresponding to solutions with equal values of the spectral parameters are found. These cases are interpreted in the context of both the algebraic and coordinate Bethe ansatz. The coordinate ansatz is generalized to the case of the XXX model of arbitrary spin.

Received: 01.07.1985

English version:
Theoretical and Mathematical Physics, 1986, Volume 69, Issue 2, Pages 1071–1079
DOI: https://doi.org/10.1007/BF01037864

Bibliographic databases:

Language: Russian

Citation: L. V. Avdeev, A. A. Vladimirov, “Exceptional solutions to the Bethe ansatz equations”, TMF, 69:2 (1986), 163–174; Theoret. and Math. Phys., 69:2 (1986), 1071–1079

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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Linking options:

https://www.mathnet.ru/eng/tmf5215

https://www.mathnet.ru/eng/tmf/v69/i2/p163

This publication is cited in the following 34 articles:

Jue Hou, Yunfeng Jiang, Rui-Dong Zhu, “Spin-$s$ rational $Q$-system”, SciPost Phys., 16:4 (2024)
Hongfei Shu, Peng Zhao, Rui-Dong Zhu, Hao Zou, “Bethe-state counting and Witten index”, SciPost Phys., 15:3 (2023)
Marius de Leeuw, Rafael I. Nepomechie, Ana L. Retore, “Flag integrable models and generalized graded algebras”, J. High Energ. Phys., 2023:6 (2023)
Rob Klabbers, Jules Lamers, “How Coordinate Bethe Ansatz Works for Inozemtsev Model”, Commun. Math. Phys., 390:2 (2022), 827
Dmitry Chernyak, Sébastien Leurent, Dmytro Volin, “Completeness of Wronskian Bethe Equations for Rational ${\mathfrak {\mathfrak {gl}}_{{{\mathsf {m}}}|{{\mathsf {n}}}}}$ Spin Chains”, Commun. Math. Phys., 391:3 (2022), 969
Charlotte Kristjansen, Dennis Müller, Konstantin Zarembo, “Duality relations for overlaps of integrable boundary states in AdS/dCFT”, J. High Energ. Phys., 2021:9 (2021)
Etienne Granet, Jesper Lykke Jacobsen, “On zero-remainder conditions in the Bethe ansatz”, J. High Energ. Phys., 2020:3 (2020)
Naoyuki Shibata, Nobuyuki Yoshioka, Hosho Katsura, “Onsager's Scars in Disordered Spin Chains”, Phys. Rev. Lett., 124:18 (2020)
Zoltán Bajnok, Etienne Granet, Jesper Lykke Jacobsen, Rafael I. Nepomechie, “On generalized Q-systems”, J. High Energ. Phys., 2020:3 (2020)
Naoyuki Shibata, Hosho Katsura, “Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model”, Phys. Rev. B, 99:22 (2019)
Gyorgy Fehér, Balázs Pozsgay, “The propagator of the finite XXZ spin-$\tfrac{1}{2}$ chain”, SciPost Phys., 6:5 (2019)
Takashi Imoto, Jun Sato, Tetsuo Deguchi, “Exact regimes of collapsed and extra two-string solutions in the two down-spin sector of the spin-1/2 massive XXZ spin chain”, J. Phys. A: Math. Theor., 52:3 (2019), 035203
Yunfeng Jiang, Yang Zhang, “Algebraic geometry and Bethe ansatz. Part I. The quotient ring for BAE”, J. High Energ. Phys., 2018:3 (2018)
Balázs Pozsgay, “Excited state correlations of the finite Heisenberg chain”, J. Phys. A: Math. Theor., 50:7 (2017), 074006
Jon Links, “Completeness of the Bethe states for the rational, spin-1/2 Richardson-Gaudin system”, SciPost Phys., 3:1 (2017)
L H Ymai, A P Tonel, A Foerster, J Links, “Quantum integrable multi-well tunneling models”, J. Phys. A: Math. Theor., 50:26 (2017), 264001
Tetsuo Deguchi, Pulak Ranjan Giri, “Exact quantum numbers of collapsed and non-collapsed two-string solutions in the spin-1/2 Heisenberg spin chain”, J. Phys. A: Math. Theor., 49:17 (2016), 174001
Anatol N. Kirillov, Reiho Sakamoto, “Bethe's quantum numbers and rigged configurations”, Nuclear Physics B, 905 (2016), 359
Anatol N. Kirillov, Reiho Sakamoto, “Some remarks on Nepomechie–Wang eigenstates for spin 1/2 XXX model”, Mosc. Math. J., 15:2 (2015), 337–352
Pulak Ranjan Giri, Tetsuo Deguchi, “Singular eigenstates in the even(odd) length Heisenberg spin chain”, J. Phys. A: Math. Theor., 48:17 (2015), 175207

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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