Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 099, 22 pages      arXiv:1605.06419      https://doi.org/10.3842/SIGMA.2016.099
Contribution to the Special Issue on Recent Advances in Quantum Integrable Systems

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

Arthur Hutsalyuk a, Andrii Liashyk bc, Stanislav Z. Pakuliak da, Eric Ragoucy e and Nikita A. Slavnov f
a) Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, Russia
b) Bogoliubov Institute for Theoretical Physics, NAS of Ukraine, Kyiv, Ukraine
c) National Research University Higher School of Economics, Russia
d) Laboratory of Theoretical Physics, JINR, Dubna, Moscow region, Russia
e) Laboratoire de Physique Théorique LAPTh, CNRS and USMB, Annecy-le-Vieux, France
f) Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Received June 24, 2016, in final form October 03, 2016; Published online October 08, 2016

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.

Key words: algebraic Bethe ansatz; superalgebras; scalar product of Bethe vectors.

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