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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 apply the nested algebraic Bethe ansatz to the models with gl(2|1) and gl}(1|2) supersymmetry. We show that form factors of local operators in these models can be expressed in terms of the universal form factors. Our derivation is based…

Mathematical Physics · Physics 2017-05-24 J. Fuksa , N. A. Slavnov

The form factor equations are solved for an SU(N) invariant S-matrix under the assumption that the anti-particle is identified with the bound state of N-1 particles. The solution is obtained explicitly in terms of the nested off-shell Bethe…

High Energy Physics - Theory · Physics 2008-11-26 Hratchia M. Babujian , Angela Foerster , Michael Karowski

We study Olshanski twisted Yangian based models, known as one-dimensional "soliton non-preserving" open spin chains, by means of algebraic Bethe ansatz. The even case, when the bulk symmetry is $\mathfrak{gl}_{2n}$ and the boundary symmetry…

Mathematical Physics · Physics 2024-10-01 Vidas Regelskis

We consider XXX spin-$1/2$ Heisenberg chain with non-diagonal boundary conditions. We obtain a compact determinant representation for the scalar product of on-shell and off-shell Bethe vectors. In the particular case when both Bethe vectors…

Mathematical Physics · Physics 2019-09-04 Samuel Belliard , Nikita A. Slavnov

We study quantum integrable models with $GL(3)$ trigonometric $R$-matrix solvable by the nested algebraic Bethe ansatz. We analyze scalar products of generic Bethe vectors and obtain an explicit representation for them in terms of a sum…

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

The algebraic Bethe ansatz can be performed rather abstractly for whole classes of models sharing the same $R$-matrix, the only prerequisite being the existence of an appropriate pseudo vacuum state. Here we perform the algebraic Bethe…

Statistical Mechanics · Physics 2017-08-16 Frank Göhmann , Alexander Seel

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 the scalar product S_{l,m} between an on-shell and an off-shell Bethe state in models with SU(3)-invariance, where l and m denote the cardinalities of the two sets of Bethe roots. We construct recursion relations relating S_{l,m}…

Mathematical Physics · Physics 2015-06-16 M Wheeler

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression…

Mathematical Physics · Physics 2014-10-23 N. Cirilo António , N. Manojlović , I. Salom

We give new combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for the evaluation modules over the Yangian $Y(\mathfrak{gl}_4)$. The case of $Y(\mathfrak{gl}_n)$ for an arbitrary $n$ is considered in…

Quantum Algebra · Mathematics 2025-07-23 Maksim Kosmakov , Vitaly Tarasov

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

Mathematical Physics · Physics 2015-09-07 S. Pakuliak , E. Ragoucy , N. A. Slavnov

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing the GL(3)-invariant R-matrix. We consider a composite model where the total monodromy matrix of the model is presented as a product of two partial…

Mathematical Physics · Physics 2015-08-03 Stanislav Pakuliak , Eric Ragoucy , Nikita A. Slavnov

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

We study Bethe vectors of integrable models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$. Starting from the super-trace formula, we exhibit recursion relations for these vectors in the case of $Y(\mathfrak{gl}(2|1))$ and…

Mathematical Physics · Physics 2017-11-23 S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

An integral presentation for the scalar products of nested Bethe vectors for the quantum integrable models associated with the quantum affine algebra $U_q(\hat{\mathfrak{gl}}_3)$ is given. This result is obtained in the framework of the…

Mathematical Physics · Physics 2010-12-15 Samuel Belliard , Stanislav Pakuliak , Eric Ragoucy

The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su(n)-invariant spin chain model with both periodic and…

High Energy Physics - Theory · Physics 2015-06-18 Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

In this paper we take further steps towards developing the separation of variables program for integrable spin chains with gl(N) symmetry. By finding, for the first time, the matrix elements of the SoV measure explicitly we were able to…

High Energy Physics - Theory · Physics 2023-01-11 Nikolay Gromov , Fedor Levkovich-Maslyuk , Paul Ryan

In this paper we formulate a general method for building completely integrable quantum systems. The method is based on the use of the so-called multi-parameter spectral equations, i.e. equations with several spectral parameters. We show…

High Energy Physics - Theory · Physics 2007-05-23 Dieter Mayer , Alexander Ushveridze

We give combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for tensor products of irreducible evaluation modules over the Yangian $Y({\mathfrak{gl}}_N)$ and the quantum affine algebra…

Quantum Algebra · Mathematics 2013-07-22 Vitaly Tarasov , Alexander Varchenko