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.
Baxter's Q-operators and operatorial Backlund flow for quantum (super)-spin chains
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abstract
We propose the operatorial form of Baxter's TQ-relations in a general form of the operatorial B\"acklund flow describing the nesting process for the inhomogeneous rational gl(K|M) quantum (super)spin chains with twisted periodic boundary conditions. The full set of Q-operators and T-operators on all levels of nesting is explicitly defined. The results are based on a generalization of the identities among the group characters and their group co-derivatives with respect to the twist matrix, found by one of the authors and P.Vieira [V.Kazakov and P.Vieira, JHEP 0810 (2008) 050 [arXiv:0711.2470]]. Our formalism, based on this new "master" identity, allows a systematic and rather straightforward derivation of the whole set of nested Bethe ansatz equations for the spectrum of quantum integrable spin chains, starting from the R-matrix.
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Classical facets of quantum integrability
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.