Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Mathematical Sciences

Scalar products of state vectors in totally asymmetric exactly solvable models on a ring

N. M. Bogoliubov

Published Jun 11, 2013• 1 citation
Publisher
DOI
10.1007/s10958-013-1368-8

Related papers

Calculation of correlation functions in totally asymmetric exactly solvable models on a ring

N. M. Bogoliubov

Theoretical and Mathematical Physics•Jun 1, 2013•3 citations

Exactly solvable models in arbitrary dimensions

Ranjan Kumar Ghosh, Sumathi Rao

arXiv:hep-th/9705141•Physics Letters A•Feb 1, 1998•17 citations

Scalar products of Bethe vectors in the models with gl(m|n) symmetry

Arthur Hutsalyuk, Andrii Nikolaevich Liashyk, Stanislav Zdislavovich Pakuliak +2 more

We study scalar products of Bethe vectors in the models solvable by the nested algebraic Bethe ansatz and described by gl(m|n) superalgebra. Using coproduct properties of the Bethe vectors we obtain a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of Bethe parameters. We also obtain recursions for the Bethe vectors. This allows us to find recursions for the highest coefficient of the scalar product.

arXiv:1704.08173•Nuclear Physics B•Aug 3, 2017•35 citations

Problems of exactly solvable model systems

N. N. Bogolyubov, A. G. Shumovskaya, A. S. Shumovskiǐ

•Jan 1, 1973•0 citations

Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 1. Super-analog of Reshetikhin formula

Arthur Hutsalyuk, Andrii Nikolaevich Liashyk, Stanislav Zdislavovich Pakuliak +2 more

We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(2|1)$ 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 $\mathfrak{gl}(1|1)$ symmetry.

arXiv:1605.09189•May 30, 2016•2 citations

Scalar products of Bethe vectors in models with gl ( 2 ∣ 1 ) symmetry 1. Super-analog of Reshetikhin formula *

Arthur Hutsalyuk, Andrii Nikolaevich Liashyk, Stanislav Zdislavovich Pakuliak +2 more

Abstract We study the scalar products of Bethe vectors in integrable models solvable by the nested algebraic Bethe ansatz and possessing 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 ) symmetry.

Journal of Physics A Mathematical and Theoretical•Oct 19, 2016•19 citations
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.
Abstract We study the scalar products of Bethe vectors in integrable models solvable by the nested algebraic Bethe ansatz and possessing 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 ) symmetry.