Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics

TL;DR

This paper demonstrates that eigenvalues of Baxter Q-operators for supersymmetric spin chains satisfy the Hirota equation, linking Bethe ansatz solutions to discrete integrable dynamics and deriving generalized Baxter equations systematically.

Contribution

It introduces a novel approach connecting supersymmetric Bethe ansatz with Hirota dynamics via Backlund transformations, enabling systematic derivation of Baxter equations.

Findings

Eigenvalues obey Hirota bilinear difference equation

Bethe ansatz as a discrete dynamical system for zeros

Systematic derivation of generalized Baxter equations

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.