Supersymmetric quantum spin chains and classical integrable systems

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.

44 pages, v2: minor corrections

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Cited by in corpus (12)

• On R-matrix valued Lax pairs for Calogero-Moser models
• On factorized Lax pairs for classical many-body integrable systems
• Solutions of ${\mathfrak{gl}}_{m|n}$ XXX Bethe ansatz equation and rational difference operators
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Lax representation of the hyperbolic van Diejen dynamics with two coupling parameters
• On the supersymmetric XXX spin chains associated to ${\mathfrak{gl}}_{1|1}$
• KZ-Calogero correspondence revisited
• Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
• On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
• Asymmetric 6-vertex model and classical Ruijsenaars-Schneider system of particles
• Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary
• Interrelations between dualities in classical integrable systems and classical-classical version of quantum-classical duality