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Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics

Vladimir Kazakov·Alexander Sorin·Anton Zabrodin
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Abstract

We show that eigenvalues of the family of Baxter Q-operators for supersymmetric integrable spin chains constructed with the gl(K|M)-invariant $R$-matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super spin chains, with any choice of simple root system, is then treated as a discrete dynamical system for zeros of polynomial solutions to the Hirota equation. Our basic tool is a chain of Backlund transformations for the Hirota equation connecting quantum transfer matrices. This approach also provides a systematic way to derive the complete set of generalized Baxter equations for super spin chains.

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Vladimir Kazakov, Alexander Sorin, Anton Zabrodin. 2007-08-18. Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics. https://doi.org/10.1016/j.nuclphysb.2007.06.025

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