Supersymmetric quantum spin chains and classical integrable systems

Zengo Tsuboi, Anton Zabrodin, Andrei Zotov

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


Abstract: For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of generating function for the family of commuting quantum transfer matrices. Any eigenvalue of the master T-operator is the tau-function of the classical mKP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0-th time of the hierarchy. This implies a remarkable relation between the quantum supersymmetric spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, we obtain a system of algebraic equations for the spectrum of the spin chain Hamiltonians.

Original languageEnglish
Article number86
JournalJournal of High Energy Physics
Issue number5
Publication statusPublished - 27 May 2015
Externally publishedYes


  • Bethe Ansatz
  • Integrable Equations in Physics
  • Integrable Hierarchies
  • Lattice Integrable Models


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