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Supersymmetric quantum spin chains and classical integrable systems
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Supersymmetric quantum spin chains and classical integrable systems
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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.
Forward citations
Cited by 2 Pith papers
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Baxter Q-operators from a Schwinger-Boson construction of the master T-operator and the mKP hierarchy
A Schwinger-boson Fock-space trace defines the gl(M) master T-operator, and the same L-operator degenerates to the Q-operator L-operator of Bazhanov–Frassek–Lukowski–Meneghelli–Staudacher.
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Revisiting B\"acklund-Darboux transformations for KP and BKP integrable hierarchies
Revisits Bäcklund-Darboux transformations for KP, BKP and related hierarchies in bilinear tau-function and fermionic operator frameworks, extending naturally to fully discrete cases.
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