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TMF, 2013, Volume 174, Number 1, Pages 59–76 (Mi tmf8373)  

This article is cited in 8 scientific papers (total in 8 papers)

The master $T$-operator for vertex models with trigonometric $R$-matrices as a classical $\tau$-function

A. V. Zabrodinabc

a Institute of Biochemical Physics, Moscow, Russia
b Institute for Theoretical and Experimental Physics, Moscow, Russia
c Higher School of Economics, Moscow, Russia

Abstract: We apply the recently proposed construction of the master $T$-operator to integrable vertex models and the associated quantum spin chains with trigonometric $R$-matrices. The master $T$-operator is a generating function for commuting transfer matrices of integrable vertex models depending on infinitely many parameters. It also turns out to be the $\tau$-function of an integrable hierarchy of classical soliton equations in the sense that it satisfies the same bilinear Hirota equations. We characterize the class of solutions of the Hirota equations that correspond to eigenvalues of the master $T$-operator and discuss its relation to the classical Ruijsenaars–Schneider system of particles.

Keywords: integrable vertex model, $R$-matrix, transfer matrix, $\tau$-function

DOI: https://doi.org/10.4213/tmf8373

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English version:
Theoretical and Mathematical Physics, 2013, 174:1, 52–67

Bibliographic databases:



Citation: A. V. Zabrodin, “The master $T$-operator for vertex models with trigonometric $R$-matrices as a classical $\tau$-function”, TMF, 174:1 (2013), 59–76; Theoret. and Math. Phys., 174:1 (2013), 52–67

Citation in format AMSBIB
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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. Anton Zabrodin, “The Master $T$-Operator for Inhomogeneous $XXX$ Spin Chain and mKP Hierarchy”, SIGMA, 10 (2014), 006, 18 pp.  mathnet  crossref  mathscinet
    2. A. Gorsky, A. Zabrodin, A. Zotov, “Spectrum of quantum transfer matrices via classical many-body systems”, J. High Energy Phys., 2014, no. 1, 070, 27 pp.  crossref  mathscinet  zmath  isi  scopus
    3. 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  elib  scopus
    4. 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
    5. Beketov M., Liashyk A., Zabrodin A., Zotov A., “Trigonometric Version of Quantum-Classical Duality in Integrable Systems”, Nucl. Phys. B, 903 (2016), 150–163  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. A. V. Zabrodin, A. V. Zotov, A. N. Liashyk, D. S. Rudneva, “Asymmetric six-vertex model and the classical Ruijsenaars–Schneider system of particles”, Theoret. and Math. Phys., 192:2 (2017), 1141–1153  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. J. W. van de Leur, A. Yu. Orlov, “Character expansion of matrix integrals”, J. Phys. A-Math. Theor., 51:2 (2018), 025208, 34 pp.  crossref  mathscinet  zmath  isi  scopus
    8. N. Rozhkovskaya, “Action of Clifford algebra on the space of sequences of transfer operators”, Algebr. Represent. Theory, 21:5 (2018), 1165–1176  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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