Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models

TL;DR

This paper derives explicit formulas for how monodromy matrix entries act on Bethe vectors in $rak{gl}(2|1)$-invariant integrable models, facilitating the study of scalar products and advancing understanding of these models.

Contribution

It provides explicit action formulas of monodromy matrix entries on Bethe vectors in $rak{gl}(2|1)$ models, a novel step for analyzing scalar products.

Findings

Actions result in finite linear combinations of Bethe vectors

Formulas enable further study of scalar products

Advances understanding of $rak{gl}(2|1)$-invariant models

Abstract

We study $\mathfrak{gl}(2|1)$ symmetric integrable models solvable by the nested algebraic Bethe ansatz. Using explicit formulas for the Bethe vectors we derive the actions of the monodromy matrix entries onto these vectors. We show that the result of these actions is a finite linear combination of Bethe vectors. The obtained formulas open a way for studying scalar products of Bethe vectors.