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Supersymmetric quantum spin chains and classical integrable systems

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arxiv 1412.2586 v2 pith:DNSY2LB2 submitted 2014-12-08 math-ph hep-thmath.MPnlin.SI

Zengo Tsuboi , Anton Zabrodin , Andrei Zotov This is my paper · ORCID
classification math-phhep-thmath.MPnlin.SI
keywords spinchainsclassicalintegrablequantumsupersymmetrichierarchymaster
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Baxter Q-operators from a Schwinger-Boson construction of the master T-operator and the mKP hierarchy

    math-ph 2026-07 accept novelty 6.0 of 10

    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.

  2. Revisiting B\"acklund-Darboux transformations for KP and BKP integrable hierarchies

    nlin.SI 2025-06 unverdicted novelty 4.0 of 10

    Revisits Bäcklund-Darboux transformations for KP, BKP and related hierarchies in bilinear tau-function and fermionic operator frameworks, extending naturally to fully discrete cases.

  3. Classical facets of quantum integrability

    math-ph 2025-01 conditional novelty 4.0 of 10

    A review showing that quantum spin chains can be solved through classical mKP soliton equations, with a new Bethe-ansatz-free proof of quantum-classical duality.

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