Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz

TL;DR

This paper explores how Backlund transformations can be used to solve the difference Hirota equation in supersymmetric spin chains, linking the nested Bethe ansatz to a sequence of transformations that simplify the problem.

Contribution

It demonstrates the equivalence between the nested Bethe ansatz and a chain of Backlund transformations for supersymmetric integrable models.

Findings

Backlund transformations facilitate solving the Hirota equation.

Nested Bethe ansatz corresponds to successive Backlund transformations.

The method simplifies the analysis of supersymmetric spin chains.

Abstract

We consider GL(K|M)-invariant integrable supersymmetric spin chains with twisted boundary conditions and elucidate the role of Backlund transformations in solving the difference Hirota equation for eigenvalues of their transfer matrices. The nested Bethe ansatz technique is shown to be equivalent to a chain of successive Backlund transformations "undressing" the original problem to a trivial one.