Symmetry, Integrability and Geometry: Methods and Applications
General information
Latest issue
Impact factor

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS


Personal entry:
Save password
Forgotten password?

SIGMA, 2014, Volume 10, 006, 18 pp. (Mi sigma871)  

This article is cited in 9 scientific papers (total in 9 papers)

The Master $T$-Operator for Inhomogeneous $XXX$ Spin Chain and mKP Hierarchy

Anton Zabrodinabcd

a Institute of Biochemical Physics, 4 Kosygina, 119334, Moscow, Russia
b ITEP, 25 B. Cheremushkinskaya, 117218, Moscow, Russia
c National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, Moscow 101000, Russia
d MIPT, Institutskii per. 9, 141700, Dolgoprudny, Moscow region, Russia

Abstract: Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master $T$-operator for the quantum inhomogeneous $GL(N)$ $XXX$ spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master $T$-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars–Schneider system of particles.

Keywords: quantum integrable spin chains; classical many-body systems; quantum-classical correspondence; master $T$-operator; tau-function.


Full text: PDF file (446 kB)
Full text:
References: PDF file   HTML file

Bibliographic databases:

ArXiv: 1310.6988
MSC: 37K10; 81Q80; 05E05
Received: October 18, 2013; in final form January 8, 2014; Published online January 11, 2014

Citation: Anton Zabrodin, “The Master $T$-Operator for Inhomogeneous $XXX$ Spin Chain and mKP Hierarchy”, SIGMA, 10 (2014), 006, 18 pp.

Citation in format AMSBIB
\by Anton~Zabrodin
\paper The Master $T$-Operator for Inhomogeneous $XXX$ Spin Chain and mKP Hierarchy
\jour SIGMA
\yr 2014
\vol 10
\papernumber 006
\totalpages 18

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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. Levin A. Olshanetsky M. Zotov A., “Relativistic Classical Integrable Tops and Quantum R-Matrices”, J. High Energy Phys., 2014, no. 7, 012  crossref  isi  scopus
    2. Levin A. Olshanetsky M. Zotov A., “Planck Constant as Spectral Parameter in Integrable Systems and Kzb Equations”, J. High Energy Phys., 2014, no. 10, 109  crossref  mathscinet  zmath  isi  scopus
    3. Galleas W., “Off-Shell Scalar Products For the Xxz Spin Chain With Open Boundaries”, Nucl. Phys. B, 893 (2015), 346–375  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. A Zabrodin, “Quantum Spin Chains and Integrable Many-Body Systems of Classical Mechanics”, Springer Proceedings in Physics, 163 (2015), 29–48  crossref  zmath  scopus
    5. Tsuboi Z. Zabrodin A. Zotov A., “Supersymmetric Quantum Spin Chains and Classical Integrable Systems”, J. High Energy Phys., 2015, no. 5, 086  crossref  mathscinet  isi  elib  scopus
    6. 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
    7. A. Zabrodin, “Quantum spin chains and classical integrable systems”, Stochastic Processes and Random Matrices, Lecture Notes of the Les Houches Summer School, 104, 2018, 578-613
    8. V. Prokofev, A. Zabrodin, “Toda lattice hierarchy and trigonometric ruijsenaars?schneider hierarchy”, J. Phys. A-Math. Theor., 52:49 (2019), 495202  crossref  mathscinet  isi
    9. V. V. Prokofev, A. V. Zabrodin, “Elliptic solutions of the Toda lattice hierarchy and the elliptic Ruijsenaars–Schneider model”, Theoret. and Math. Phys., 208:2 (2021), 1093–1115  mathnet  crossref  crossref  isi  elib
  • Symmetry, Integrability and Geometry: Methods and Applications
    Number of views:
    This page:432
    Full text:41

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022