A note on $\mathfrak{gl}_2$-invariant Bethe vectors

TL;DR

This paper studies how $rak{gl}_2$-invariant Bethe vectors behave under twist transformations in quantum integrable models, providing formulas for their transformations and actions.

Contribution

It demonstrates the preservation of on-shell Bethe vector structures under twist transformations and derives explicit actions of twisted monodromy matrix entries.

Findings

On-shell Bethe vectors are preserved under certain twists.

Explicit formulas for actions of twisted monodromy entries.

Enhances understanding of symmetry transformations in integrable models.

Abstract

We consider $\mathfrak{gl}_2$-invariant quantum integrable models solvable by the algebraic Bethe ansatz. We show that the form of on-shell Bethe vectors is preserved under certain twist transformations of the monodromy matrix. We also derive the actions of the twisted monodromy matrix entries onto twisted off-shell Bethe vectors.