Journal of High Energy Physics

, 2013:64 | Cite as

Classical tau-function for quantum spin chains

  • Alexander Alexandrov
  • Vladimir Kazakov
  • Sebastien LeurentEmail author
  • Zengo Tsuboi
  • Anton Zabrodin
Open Access


For an arbitrary generalized quantum integrable spin chain we introduce a “master T -operator” which represents a generating function for commuting quantum transfer matrices constructed by means of the fusion procedure in the auxiliary space. We show that the functional relations for the transfer matrices are equivalent to an infinite set of model-independent bilinear equations of the Hirota form for the master T -operator, which allows one to identify it with τ -function of an integrable hierarchy of classical soliton equations. In this paper we consider spin chains with rational GL(N)-invariant R-matrices but the result is independent of a particular functional form of the transfer matrices and directly applies to quantum integrable models with more general (trigonometric and elliptic) R-matrices and to supersymmetric spin chains.


Integrable Equations in Physics Lattice Integrable Models 


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Copyright information

© SISSA 2013

Authors and Affiliations

  • Alexander Alexandrov
    • 1
    • 2
  • Vladimir Kazakov
    • 3
    • 4
  • Sebastien Leurent
    • 4
    • 8
    Email author
  • Zengo Tsuboi
    • 5
    • 9
  • Anton Zabrodin
    • 2
    • 6
    • 7
  1. 1.Mathematisches Institut, Albert-Ludwigs-UniversitätFreiburgGermany
  2. 2.ITEPMoscowRussia
  3. 3.Université Paris 6ParisFrance
  4. 4.École Normale SupérieureParisFrance
  5. 5.Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, Johann von Neumann-HausBerlinGermany
  6. 6.Institute of Biochemical PhysicsMoscowRussia
  7. 7.National Research University Higher School of EconomicsMoscowRussia
  8. 8.Institut de Mathématiques de BourgogneUniversité de BourgogneDijonFrance
  9. 9.Department of Theoretical Physics, Research School of Physics and EngineeringAustralian National UniversityCanberraAustralia

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