Scalar products and norm of Bethe vectors for integrable models based on $U_q(\widehat{\mathfrak{gl}}_{n})$
A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov
SciPost Phys. 4, 006 (2018) · published 30 January 2018
- doi: 10.21468/SciPostPhys.4.1.006
- Submissions/Reports
-
Abstract
We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_{n})$. We also present a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of the Bethe parameters, whose factors are characterized by two highest coefficients. We provide different recursions for these highest coefficients. In addition, we show that when the Bethe vectors are on-shell, their norm takes the form of a Gaudin determinant.
Cited by 10

Ontology / Topics
See full Ontology or Topics database.Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 2 Arthur Hutsalyuk,
- 3 4 5 Andrii Liashyk,
- 1 6 Stanislav Pakuliak,
- 7 Eric Ragoucy,
- 8 Nikita Slavnov
- 1 Московский физико-технический институт / Moscow Institute of Physics and Technology [MIPT (SU)]
- 2 Bergische Universität Wuppertal / University of Wuppertal [BUW]
- 3 Bogolyubov Institute for Theoretical Physics [BITP]
- 4 Высшая школа экономики / National Research University Higher School of Economics [HSE]
- 5 Skolkovo Institute of Science and Technology [Skoltech]
- 6 Объединённый институт ядерных исследований / Joint Institute for Nuclear Research [JINR]
- 7 Laboratoire d'Annecy-le-Vieux de Physique Théorique [LAPTh]
- 8 Математический институт им. В. А. Стеклова / Steklov Mathematical Institute
- Centre National de la Recherche Scientifique / French National Centre for Scientific Research [CNRS]
- Ministry of Education and Science of the Russian Federation (through Organization: Министерство образования и науки Российской Федерации / The Ministry of Education and Science of the Russian Federation)
- Российский фонд фундаментальных исследований / Russian Foundation for Basic Research [RFBR]