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The algebraic Bethe ansatz is a powerful method to diagonalize transfer-matrices of statistical models derived from solutions of (graded) Yang Baxter equations, connected to fundamental representations of Lie (super-)algebras and their…

Condensed Matter · Physics 2009-10-31 J. Gruneberg

In this paper we apply the nested algebraic Bethe ansatz to compute the eigenvalues and the Bethe equations of the transfer matrix of the new integrable Lindbladian found in [1]. We show that it can be written as an integrable spin chain…

Statistical Mechanics · Physics 2022-07-29 Marius de Leeuw , Chiara Paletta

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

The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed previously in the literature: the anharmonic oscillator, the…

Mathematical Physics · Physics 2024-09-17 Siyu Li , Ian Marquette , Yao-Zhong Zhang

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 off-diagonal Bethe ansatz method is generalized to the high spin integrable systems associated with the su(2) algebra by employing the spin-s isotropic Heisenberg chain model with generic integrable boundaries as an example. With the…

Statistical Mechanics · Physics 2015-06-19 Junpeng Cao , Shuai Cui , Wen-Li Yang , Kangjie Shi , Yupeng Wang

The Bethe Ansatz is a method for constructing exact eigenstates of quantum-integrable spin chains. Recently, deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the…

Quantum Physics · Physics 2025-07-29 Roberto Ruiz , Alejandro Sopena , Esperanza López , Germán Sierra , Balázs Pozsgay

The Algebraic Bethe ansatz for a supersymmetric nineteen vertex-model constructed from a three-dimensional representation of the twisted quantum affine Lie superalgebra $\mathcal{U}_{q}[\mathrm{osp}(2|2)^{(2)}]$ is presented in detail. The…

Exactly Solvable and Integrable Systems · Physics 2019-08-22 G. K. Sampa , A. Lima-Santos

A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…

Strongly Correlated Electrons · Physics 2015-06-24 X. -W. Guan , A. Foerster , J. Links , H. -Q Zhou , A. Prestes Tonel , R. H. McKenzie

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an…

Strongly Correlated Electrons · Physics 2009-10-30 Anthony J. Bracken , Xiang-Yu Ge , Yao-Zhong Zhang , Huan-Qiang Zhou

We give a detailed description of the nested algebraic Bethe ansatz. We consider integrable models with a $\mathfrak{gl}_3$-invariant $R$-matrix as the basic example, however, we also describe possible generalizations. We give recursions…

Mathematical Physics · Physics 2020-09-02 N. A. Slavnov

A strongly correlated electron system associated with the quantum superalgebra ${U}_q[{osp}(2|2)]$ is studied in the framework of the quantum inverse scattering method. By solving the graded reflection equation, two classes of…

Strongly Correlated Electrons · Physics 2016-08-16 X. -W. Guan , A. Foerster , U. Grimm , R. A. Römer , M. Schreiber

The fused six-vertex models with open boundary conditions are studied. The Bethe ansatz solution given by Sklyanin has been generalized to the transfer matrices of the fused models. We have shown that the eigenvalues of transfer matrices…

High Energy Physics - Theory · Physics 2010-01-07 Yu-Kui Zhou

We present a thorough analysis of the Non Intersecting String (NIS) model and its exact solution. This is an integrable $q$-states vertex model describing configurations of non-intersecting polygons on the lattice. The exact eigenvalues of…

High Energy Physics - Theory · Physics 2009-10-22 H. J. de Vega , G. Giavarini

New classes of integrable boundary conditions for the q-deformed (or two-parameter) supersymmetric U model are presented. The boundary systems are solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are…

Strongly Correlated Electrons · Physics 2009-10-30 Yao-Zhong Zhang , Huan-Qiang Zhou

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU(3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q…

Mathematical Physics · Physics 2018-06-27 Pei Sun , Zhirong Xin , Yi Qiao , Fakai Wen , Kun Hao , Junpeng Cao , Guang-Liang Li , Tao Yang , Wen-Li Yang , Kangjie Shi

We introduce novel polynomial deformations of the Lie algebra $sl(2)$. We construct their finite-dimensional irreducible representations and the corresponding differential operator realizations. We apply our results to a class of spin…

Mathematical Physics · Physics 2025-09-16 Siyu Li , Ian Marquette , Yao-Zhong Zhang

We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of…

Mathematical Physics · Physics 2017-05-24 Azat M. Gainutdinov , Wenrui Hao , Rafael I. Nepomechie , Andrew J. Sommese

We present in an unified and detailed way the Nested Bethe Ansatz for closed spin chains based on Y(gl(n)), Y(gl(m|n)), U_q(gl(n)) or U_q(gl(m|n)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain. In…

Mathematical Physics · Physics 2010-04-07 S. Belliard , E. Ragoucy

We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an…

Mathematical Physics · Physics 2009-11-11 D. Arnaudon , N. Crampe , A. Doikou , L. Frappat , E. Ragoucy