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arXiv:1605.06419 · Symmetry Integrability and Geometry Methods and Applications

Multiple Actions of the Monodromy Matrix in gl(2|1)-Invariant Integrable Models

Arthur Hutsalyuk, Andrii Nikolaevich Liashyk, Stanislav Zdislavovich Pakuliak, JINR, Dubna, Russia, E. Ragoucy, Laboratoire de Physique Théorique LAPTh, CNRS and USMB, France, Никита Андреевич Славнов

Published Oct 8, 2016• 26 citations
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Abstract

We study 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.

DOI
10.3842/sigma.2016.099

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Scalar products of Bethe vectors in models with gl(2∣1)\mathfrak{gl}(2|1)gl(2∣1) symmetry 1. Super-analog of Reshetikhin formula
We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing gl(2∣1)\mathfrak{gl}(2|1)gl(2∣1) symmetry. Using explicit formulas of the monodromy matrix entries multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with gl(1∣1)\mathfrak{gl}(1|1)gl(1∣1) symmetry.
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