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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 consider quantum integrable models associated with $\mathfrak{so}_3$ algebra. We describe Bethe vectors of these models in terms of the current generators of the $\mathcal{D}Y(\mathfrak{so}_3)$ algebra. To implement this approach we use…

Mathematical Physics · Physics 2019-11-19 A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

Multiple actions of the monodromy matrix elements onto off-shell Bethe vectors in the $\mathfrak{gl}(m|n)$-invariant quantum integrable models are calculated. These actions are used to describe recursions for the highest coefficients in the…

Mathematical Physics · Physics 2021-12-13 A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

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

The first goal of this paper is to give a precise and simple definition for off-shell Bethe vectors in a generic $g$-invariant integrable model for $g=gl_n$, $o_{2n+1}$, $sp_{2n}$ and $o_{2n}$. We prove from our definition that the…

Mathematical Physics · Physics 2026-01-05 A. Liashyk , S. Pakuliak , E. Ragoucy

A class of $\mathfrak{o}_{2n+1}$-invariant quantum integrable models is investigated in the framework of algebraic Bethe ansatz method. A construction of the $\mathfrak{o}_{2n+1}$-invariant Bethe vector is proposed in terms of the Drinfeld…

Mathematical Physics · Physics 2021-12-13 A. Liashyk , S. Z. Pakuliak

We consider $\mathfrak{gl}_2$-invariant quantum integrable models solvable by the algebraic Bethe ansatz. We show that the form of on-shell Bethe vectors is preserved under certain twist transformations of the monodromy matrix. We also…

Mathematical Physics · Physics 2019-09-09 S. Belliard , N. A. Slavnov

We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}_3$-invariant $R$-matrix. We study a new recently proposed approach to construct on-shell Bethe vectors of these models. We…

Mathematical Physics · Physics 2018-07-04 A. Liashyk , N. A. Slavnov

We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(N)$-invariant $R$-matrix. We study two types of Bethe vectors. The first type corresponds to the original monodromy matrix.…

Mathematical Physics · Physics 2019-05-22 A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

We study quantum integrable models with GL(3) trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz. Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the…

Mathematical Physics · Physics 2013-10-08 Samuel Belliard , Stanislav Pakuliak , Eric Ragoucy , Nikita A. Slavnov

We consider quantum integrable models solvable by the algebraic Bethe ansatz and possessing $\mathfrak{gl}(2)$-invariant $R$-matrix. We study the models of both periodic boundary conditions and boundary conditions based on reflection…

Mathematical Physics · Physics 2019-07-30 A. Liashyk

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

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 study quantum Uq(gl(N)) integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the right and left universal off-shell nested Bethe vectors. It is shown that these formulas can be related by…

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

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing GL(3)-invariant R-matrix. We obtain determinant representations for form factors of off-diagonal entries of the monodromy matrix. These representations…

Mathematical Physics · Physics 2015-06-18 S. Pakuliak , E. Ragoucy , N. A. Slavnov

The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…

Mathematical Physics · Physics 2015-06-09 Yupeng Wang , Wen-Li Yang , Junpeng Cao , Kangjie Shi

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

Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, a systematic method for retrieving the Bethe-type eigenstates of integrable models without obvious reference state is developed by employing certain…

Mathematical Physics · Physics 2015-07-16 Xin Zhang , Yuan-Yuan Li , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

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
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