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.
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Tsuboi, Z., Zabrodin, A. & Zotov, A. Supersymmetric quantum spin chains and classical integrable systems. J. High Energ. Phys. 2015, 86 (2015). https://doi.org/10.1007/JHEP05(2015)086
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DOI: https://doi.org/10.1007/JHEP05(2015)086