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

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• Scalar product of twisted XXX modified Bethe vectors
• On the supersymmetric XXX spin chains associated to ${\mathfrak{gl}}_{1|1}$
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Bethe Vectors for Composite Models with $\mathfrak{gl}(2|1)$ and $\mathfrak{gl}(1|2)$ Supersymmetry
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• Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 1. Super-analog of Reshetikhin formula
• Action of the monodromy matrix entries in the generalized algebraic Bethe ansatz