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Related papers: On Bethe vectors in $\mathfrak{gl}_3$-invariant in…

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We study quantum integrable GL(3)-based models with a trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. We derive a determinant representation for a special case of scalar products of Bethe vectors. This representation…

Mathematical Physics · Physics 2015-03-23 N. A. Slavnov

In this work we have developed the essential tools for the algebraic Bethe ansatz solution of integrable vertex models invariant by a unique U(1) charge symmetry. The formulation is valid for arbitrary statistical weights and respective…

Mathematical Physics · Physics 2009-11-13 C. S. Melo , M. J. Martins

We show that the scalar products of on-shell and off-shell Bethe vectors in the algebra1ic Bethe ansatz solvable models satisfy a system of linear equations. We find solutions to this system for a wide class of integrable models. We also…

Mathematical Physics · Physics 2020-01-08 S. Belliard , N. A. Slavnov

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…

Mathematical Physics · Physics 2016-11-24 A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

We apply the algebraic Bethe ansatz developed in our previous paper \cite{CM} to three different families of U(1) integrable vertex models with arbitrary $N$ bond states. These statistical mechanics systems are based on the higher spin…

Mathematical Physics · Physics 2009-08-03 M. J. Martins , C. S. Melo

This short note corresponds to a talk given at "Lie Theory and Its Applications in Physics", (Varna, Bulgaria, June 2013) and is based on joint works with S. Belliard, S. Pakuliak and N. Slavnov, see arXiv:1206.4931, arXiv:1207.0956,…

Mathematical Physics · Physics 2015-03-11 E. Ragoucy

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing $GL(3)$-invariant $R$-matrix. Assuming that the monodromy matrix of the model can be expanded into series with respect to the inverse spectral…

Mathematical Physics · Physics 2015-05-20 S. Pakuliak , E. Ragoucy , N. A. Slavnov

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain determinant representations for form factors of diagonal entries of the monodromy matrix. This representation can be used for the calculation of…

Mathematical Physics · Physics 2015-06-12 S. Belliard , S. Pakuliak , E. Ragoucy , N. A. Slavnov

We diagonalize the transfer matrix of a solvable vertex model constructed by combining the vector representation of U_q[Sl(n|m)] and its dual by means of the quantum inverse scattering framework. The algebraic Bethe ansatz solution consider…

Exactly Solvable and Integrable Systems · Physics 2008-11-26 G. A. P. Ribeiro , M. J. Martins

We compute scalar products of off-shell Bethe vectors in models with $o_{2n+1}$ symmetry. The scalar products are expressed as a sum over partitions of the Bethe parameter sets, the building blocks being the so-called highest coefficients.…

Mathematical Physics · Physics 2025-07-23 A. Liashyk , S. Pakuliak , E. Ragoucy

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…

Mathematical Physics · Physics 2016-10-11 Arthur Hutsalyuk , Andrii Liashyk , Stanislav Z. Pakuliak , Eric Ragoucy , Nikita A. Slavnov

We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe…

Statistical Mechanics · Physics 2011-07-28 M. Kormos , G. Mussardo , B. Pozsgay

Supersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe ansatz are studied. Using a coproduct in the bialgebra of monodromy matrix elements and their action on Bethe vectors, formulas for Bethe vectors…

Mathematical Physics · Physics 2017-03-14 Jan Fuksa

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…

Mathematical Physics · Physics 2018-03-01 A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

A new method is introduced to derive general recurrence relations for off-shell Bethe vectors in quantum integrable models with either type $\mathfrak{gl}_n$ or type $\mathfrak{o}_{2n+1}$ symmetries. These recurrence relations describe how…

Quantum Algebra · Mathematics 2025-09-23 Andrii Liashyk , Stanislav Pakuliak , Eric Ragoucy

We study quantum integrable models with GL(3) trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of the highest…

Mathematical Physics · Physics 2015-06-17 S. Pakuliak , E. Ragoucy , N. A. Slavnov

In this work we present a general construction of integrable models for boson tunneling in multi-well systems. We show how the models may be derived through the Quantum Inverse Scattering Method and solved by algebraic Bethe ansatz means.…

Mathematical Physics · Physics 2017-06-13 L H Ymai , A P Tonel , A Foerster , J Links

We construct integrable generalised models in a systematic way exploring different representations of the gl(N) algebra. The models are then interpreted in the context of atomic and molecular physics, most of them related to different types…

Strongly Correlated Electrons · Physics 2010-10-27 A. Foerster , E. Ragoucy

The term Bethe Ansatz stands for a multitude of methods in the theory of integrable models in statistical mechanics and quantum field theory that were designed to study the spectra, the thermodynamic properties and the correlation functions…

Mathematical Physics · Physics 2024-12-31 Frank Göhmann

We reformulate nested relations between off-shell $U_q(\widehat{\mathfrak{gl}}_N)$ Bethe vectors as a certain equation on generating series of strings of the composed $U_q(\widehat{\mathfrak{gl}}_N)$ currents. Using inversion of the…

Quantum Algebra · Mathematics 2008-11-24 Sergey Khoroshkin , Stanislav Pakuliak