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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 obtain a determinant representation of normalized scalar products of on-shell and off-shell Bethe vectors in the inhomogeneous 8-vertex model. We consider the case of rational anisotropy parameter and use the generalized algebraic Bethe…

Mathematical Physics · Physics 2022-07-15 N. Slavnov , A. Zabrodin , A. Zotov

We consider integrable models solved by the nested algebraic Bethe ansatz and associated with $\mathfrak{gl}(2|1)$ or $\mathfrak{gl}(3)$ algebra symmetry. The analogue of sum formulae, previously formulated for scalar products, is…

High Energy Physics - Theory · Physics 2021-02-10 Arthur Hutsalyuk , Andrii Liashyk

We compute scalar products and norms of Bethe vectors in the massless sector of AdS_3 integrable superstring theories, by exploiting the general difference form of the S-matrix of massless excitations in the pure Ramond-Ramond case, and the…

High Energy Physics - Theory · Physics 2019-11-26 Juan Miguel Nieto , Alessandro Torrielli

We consider an $XYZ$ spin chain within the framework of the generalized algebraic Bethe ansatz. We study scalar products of the transfer matrix eigenvectors and arbitrary Bethe vectors. In the particular case of free fermions we obtain…

Mathematical Physics · Physics 2023-06-23 G. Kulkarni , N. A. Slavnov

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

In this work we use the algebraic Bethe ansatz to derive the general scalar product in the six-vertex model for generic Boltzmann weights. We performed this calculation using only the unitarity property, the Yang-Baxter algebra and the…

Exactly Solvable and Integrable Systems · Physics 2013-06-25 G. A. P. Ribeiro

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 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 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

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

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 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

In this work the scalar product of Bethe vectors for the six-vertex model is studied by means of functional equations. The scalar products are shown to obey a system of functional equations originated from the Yang-Baxter algebra and its…

Mathematical Physics · Physics 2013-12-25 W. Galleas

We derive explicit formulas for solutions of the Bethe Ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector representation for all simple Lie algebras of…

Quantum Algebra · Mathematics 2016-11-03 Kang Lu , E. Mukhin , A. Varchenko

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

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 construct a canonical isomorphism between the Bethe algebra acting on a multiplicity space of a tensor product of evaluation gl_N[t]-modules and the scheme-theoretic intersection of suitable Schubert varieties. Moreover, we prove that…

Quantum Algebra · Mathematics 2007-11-27 E. Mukhin , V. Tarasov , A. Varchenko

We consider closed XXX spin chains with broken total spin $U(1)$ symmetry within the framework of the modified algebraic Bethe ansatz. We study multiple actions of the modified monodromy matrix entries on the modified Bethe vectors. The…

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

We consider an open spin chain model with GL(N) bulk symmetry that is broken to GL(M) x GL(N-M) by the boundary, which is a generalization of a model arising in string/gauge theory. We prove the integrability of this model by constructing…

High Energy Physics - Theory · Physics 2015-05-14 Rafael I. Nepomechie