Bethe Vectors for Composite Models with $\mathfrak{gl}(2|1)$ and $\mathfrak{gl}(1|2)$ Supersymmetry

TL;DR

This paper develops formulas for Bethe vectors in supersymmetric composite quantum integrable models based on super-Yangians, advancing the algebraic Bethe ansatz method for these complex systems.

Contribution

It introduces a coproduct approach to construct Bethe vectors in composite models with $rak{gl}(2|1)$ and $rak{gl}(1|2)$ supersymmetry, providing explicit formulas.

Findings

Formulas for Bethe vectors in supersymmetric models derived

Application of coproduct in the bialgebra of monodromy matrix elements

Enhanced understanding of algebraic Bethe ansatz for super-Yangians

Abstract

Supersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe ansatz are studied. Using a coproduct in the bialgebra of monodromy matrix elements and their action on Bethe vectors, formulas for Bethe vectors in the composite models with supersymmetry based on the super-Yangians $Y[\mathfrak{gl}(2|1)]$ and $Y[\mathfrak{gl}(1|2)]$ are derived.