A. V. Zabrodin, “Hirota equation and Bethe ansatz”, TMF, 116:1 (1998), 54–100; Theoret. and Math. Phys., 116:1 (1998), 782

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Teoreticheskaya i Matematicheskaya Fizika, 1998, Volume 116, Number 1, Pages 54–100
DOI: https://doi.org/10.4213/tmf889 (Mi tmf889)

This article is cited in 22 scientific papers (total in 22 papers)

Hirota equation and Bethe ansatz

A. V. Zabrodin^ab

^a N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences
^b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Full-text PDF (482 kB) Citations (22)

DOI: https://doi.org/10.4213/tmf889

Abstract: Recent analyses of classical integrable structures in quantum integrable models solved by various versions of the Bethe ansatz are reviewed. Similarities between elements of quantum and classical theories of integrable systems are discussed. Some key ideas in quantum theory, now standard in the quantum inverse scattering method, are identified with typical constructions in classical soliton theory. Functional relations for quantum transfer matrices become the classical Hirota bilinear difference equation; solving this classical equation gives all the basic results for the spectral properties of quantum systems. Vice versa, typical Bethe ansatz formulas under certain boundary conditions yield solutions of this classical equation. The Baxter

T

$T$ -

Q

$Q$ relation and its generalizations arise as auxiliary linear problems for the Hirota equation.

Received: 28.01.1998

English version:
Theoretical and Mathematical Physics, 1998, Volume 116, Issue 1, Pages 782–819
DOI: https://doi.org/10.1007/BF02557123

Bibliographic databases:

Language: Russian

Citation: A. V. Zabrodin, “Hirota equation and Bethe ansatz”, TMF, 116:1 (1998), 54–100; Theoret. and Math. Phys., 116:1 (1998), 782–819

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf889

https://doi.org/10.4213/tmf889

https://www.mathnet.ru/eng/tmf/v116/i1/p54

This publication is cited in the following 22 articles:

Ilievski E., De Nardis J., Gopalakrishnan S., Vasseur R., Ware B., “Superuniversality of Superdiffusion”, Phys. Rev. X, 11:3 (2021), 031023
Gerdjikov V.S. Smirnov A.O. Matveev V.B., “From Generalized Fourier Transforms to Spectral Curves For the Manakov Hierarchy. i. Generalized Fourier Transforms”, Eur. Phys. J. Plus, 135:8 (2020), 659
Maillet J.M. Niccoli G. Vignoli L., “Separation of Variables Bases For Integrable Gl(M Vertical Bar N) and Hubbard Models”, SciPost Phys., 9:4 (2020), 060
Ilievski E. Quinn E., “The Equilibrium Landscape of the Heisenberg Spin Chain”, SciPost Phys., 7:3 (2019), 033
Fioravanti D. Nepomechie R.L., “An inhomogeneous Lax representation for the Hirota equation”, J. Phys. A-Math. Theor., 50:5 (2017), 054001
Kazakov V. Leurent S., “Finite Size Spectrum of Su(N) Principal Chiral Field From Discrete Hirota Dynamics”, Nucl. Phys. B, 902 (2016), 354–386
Zengo Tsuboi, Anton Zabrodin, Andrei Zotov, “Supersymmetric quantum spin chains and classical integrable systems”, JHEP, 2015, no. 5, 86–43
A. Zabrodin, Springer Proceedings in Physics, 163, Nonlinear Mathematical Physics and Natural Hazards, 2015, 29
A. Zabrodin, A. Zotov, “Classical-quantum correspondence and functional relations for Painlevé equations”, Constr. Approx., 41:3 (2015), 385–423
Anton Zabrodin, “The Master $T$-Operator for Inhomogeneous $XXX$ Spin Chain and mKP Hierarchy”, SIGMA, 10 (2014), 006, 18 pp.
Alexandrov A. Leurent S. Tsuboi Z. Zabrodin A., “The Master T-Operator For the Gaudin Model and the KP Hierarchy”, Nucl. Phys. B, 883 (2014), 173–223
Zabrodin A., “Quantum Gaudin Model and Classical KP Hierarchy”, Physics and Mathematics of Nonlinear Phenomena 2013, Journal of Physics Conference Series, 482, IOP Publishing Ltd, 2014, 012047
A. V. Zabrodin, “The master $T$-operator for vertex models with trigonometric $R$-matrices as a classical $\tau$-function”, Theoret. and Math. Phys., 174:1 (2013), 52–67
Alexandrov A. Kazakov V. Leurent S. Tsuboi Z. Zabrodin A., “Classical Tau-Function for Quantum Spin Chains”, J. High Energy Phys., 2013, no. 9, 064
Hegedus, A, “Discrete Hirota dynamics for AdS/CFT”, Nuclear Physics B, 825:3 (2010), 341
Gromov, N, “Finite volume spectrum of 2D field theories from Hirota dynamics”, Journal of High Energy Physics, 2009, no. 12, 060
A. V. Zabrodin, “Bäcklund transformations for the difference Hirota equation and the supersymmetric Bethe ansatz”, Theoret. and Math. Phys., 155:1 (2008), 567–584
Kazakov, V, “Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics”, Nuclear Physics B, 790:3 (2008), 345
Habibullin I., “Characteristic Algebras of Discrete Equations”, Difference Equations, Special Functions and Orthogonal Polynomials, 2007, 249–257
I. T. Habibullin, “C-Series Discrete Chains”, Theoret. and Math. Phys., 146:2 (2006), 170–182

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

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