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Baxter’s Q-operators and Operatorial Bäcklund Flow for Quantum (Super)-Spin Chains

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Abstract

We propose the operatorial Baxter’s TQ-relations in a general form of the operatorial Bäcklund 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 Kazakov and Vieira (JHEP 0810:050, 2008). 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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Author notes

  1. Zengo Tsuboi

    Present address: Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, Johann von Neumann-Haus, Rudower Chaussee 25, 12489, Berlin, Germany

Authors and Affiliations

  1. Ecole Normale Superieure, LPT, 75231, Paris Cedex-5, France

    Vladimir Kazakov & Sebastien Leurent

  2. Université Paris-VI, Paris, France

    Vladimir Kazakov

  3. Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476, Potsdam, Germany

    Zengo Tsuboi

  4. Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

    Zengo Tsuboi

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  1. Vladimir Kazakov
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  2. Sebastien Leurent
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  3. Zengo Tsuboi
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Correspondence to Sebastien Leurent.

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Communicated by P. Forrester

Member of Institut Universitaire de France.

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Kazakov, V., Leurent, S. & Tsuboi, Z. Baxter’s Q-operators and Operatorial Bäcklund Flow for Quantum (Super)-Spin Chains. Commun. Math. Phys. 311, 787–814 (2012). https://doi.org/10.1007/s00220-012-1428-9

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