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TMF, 2008, Volume 155, Number 1, Pages 74–93 (Mi tmf6194)  

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

Bäcklund transformations for the difference Hirota equation and the supersymmetric Bethe ansatz

A. V. Zabrodinab

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b Institute of biochemical physics of the Russian Academy of Sciences

Abstract: We consider $GL(K\mid M)$-invariant integrable supersymmetric spin chains with twisted boundary conditions and demonstrate the role of Bäcklund transformations in solving the difference Hirota equation for eigenvalues of their transfer matrices. We show that the nested Bethe ansatz technique is equivalent to a chain of successive Bäcklund transformations "undressing" the original problem to a trivial one.

Keywords: integrable nonlinear difference equation, Bäcklund transformation, integrable supersymmetric spin chain, Bethe ansatz

DOI: https://doi.org/10.4213/tmf6194

Full text: PDF file (557 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 155:1, 567–584

Bibliographic databases:


Citation: A. V. Zabrodin, “Bäcklund transformations for the difference Hirota equation and the supersymmetric Bethe ansatz”, TMF, 155:1 (2008), 74–93; Theoret. and Math. Phys., 155:1 (2008), 567–584

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6194
  • http://mi.mathnet.ru/eng/tmf/v155/i1/p74

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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. Bazhanov V.V., Tsuboi Z., “Baxter's Q-operators for supersymmetric spin chains”, Nuclear Phys. B, 805:3 (2008), 451–516  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    2. Tsuboi Z., “Solutions of the $T$-system and Baxter equations for supersymmetric spin chains”, Nuclear Phys. B, 826:3 (2010), 399–455  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. Kazakov V., Leurent S., Tsuboi Z., “Baxter's Q-Operators and Operatorial Backlund Flow for Quantum (Super)-Spin Chains”, Commun. Math. Phys., 311:3 (2012), 787–814  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    4. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. 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  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. Tsuboi Z., “Wronskian Solutions of the T-, Q- and Y-Systems Related to Infinite Dimensional Unitarizable Modules of the General Linear Superalgebra Gl(M Vertical Bar N)”, Nucl. Phys. B, 870:1 (2013), 92–137  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    7. Anton Zabrodin, “The Master $T$-Operator for Inhomogeneous $XXX$ Spin Chain and mKP Hierarchy”, SIGMA, 10 (2014), 006, 18 pp.  mathnet  crossref  mathscinet
    8. A. K. Pogrebkov, “Hirota difference equation: Inverse scattering transform, Darboux transformation, and solitons”, Theoret. and Math. Phys., 181:3 (2014), 1585–1598  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. 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  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. 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  crossref  isi  scopus  scopus
    11. Kazakov V., Leurent S., “Finite Size Spectrum of Su(N) Principal Chiral Field From Discrete Hirota Dynamics”, Nucl. Phys. B, 902 (2016), 354–386  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    12. A. K. Pogrebkov, “Commutator identities on associative algebras, the non-Abelian Hirota difference equation and its reductions”, Theoret. and Math. Phys., 187:3 (2016), 823–834  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    13. Jiang Yu., Komatsu Sh., Kostov I., Serban D., “Clustering and the three-point function”, J. Phys. A-Math. Theor., 49:45 (2016), 454003  crossref  mathscinet  zmath  isi  elib  scopus
    14. Kazakov V., Leurent S., Volin D., “T-System on T-Hook : Grassmannian Solution and Twisted Quantum Spectral Curve”, J. High Energy Phys., 2016, no. 12, 044  crossref  mathscinet  isi  scopus  scopus
    15. Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.  mathnet  crossref  mathscinet
    16. A. K. Pogrebkov, “Higher Hirota difference equations and their reductions”, Theoret. and Math. Phys., 197:3 (2018), 1779–1796  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    17. Pogrebkov A., “Hirota Difference Equation and Darboux System: Mutual Symmetry”, Symmetry-Basel, 11:3 (2019), 436  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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