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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

Recently, the XXX spin chain with arbitrary boundary fields was successfully solved [1] via the off-diagonal Bethe ansatz method [2]. The correctness and the completeness of this solution were numerically verified by Nepomechie for one…

Statistical Mechanics · Physics 2013-09-26 Yuzhu Jiang , Shuai Cui , Junpeng Cao , Wen-Li Yang , Yupeng Wang

The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the $SU(2|2)$ vertex model with…

Mathematical Physics · Physics 2020-10-28 Xiaotian Xu , Junpeng Cao , Yi Qiao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values i \pi/(p+1), where p is a positive integer. All six boundary parameters are…

High Energy Physics - Theory · Physics 2011-02-16 Rajan Murgan , Rafael I. Nepomechie , Chi Shi

The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator…

Mathematical Physics · Physics 2022-12-27 Guang-Liang Li , Junpeng Cao , Panpan Xue , Kun Hao , Pei Sun , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a…

Mathematical Physics · Physics 2011-02-16 Daniel Arnaudon , Nicolas Crampe , Anastasia Doikou , Luc Frappat , Eric Ragoucy

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

We propose an expression for the eigenvalues of the transfer matrix for the $U_q(B_n)$-invariant open quantum spin chain associated with the fundamental representation of $A^{(2)}_{2n}$. By assumption, the Bethe Ansatz equations are…

High Energy Physics - Theory · Physics 2015-06-26 Simone Artz , Luca Mezincescu , Rafael I. Nepomechie

We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of…

Statistical Mechanics · Physics 2011-03-07 Holger Frahm , Jan H. Grelik , Alexander Seel , Tobias Wirth

We revisit the construction of the eigenvectors of the single and double-row transfer matrices associated with the Zamolodchikov-Fateev model, within the algebraic Bethe ansatz method. The left and right eigenvectors are constructed using…

Mathematical Physics · Physics 2018-04-27 Antonio Lima-Santos , Rafael I. Nepomechie , Rodrigo A. Pimenta

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 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

For generic values of q, all the eigenvectors of the transfer matrix of the U_q sl(2)-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin. However, when q is…

Mathematical Physics · Physics 2017-05-24 Azat M. Gainutdinov , Rafael I. Nepomechie

A non homogeneous spin chain in the representations $ \{3 \}$ and $ \{3^*\}$ of $A_2$ is analyzed. We find that the naive nested Bethe ansatz is not applicable to this case. A method inspired in the nested Bethe ansatz, that can be applied…

High Energy Physics - Theory · Physics 2009-10-30 Julio Abad , Miguel Rios

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 discuss some fundamental properties of the XXZ spin chain, which are important in the algebraic Bethe-ansatz derivation for the multiple-integral representations of the spin-s XXZ correlation function with an arbitrary product of…

Statistical Mechanics · Physics 2017-08-23 Tetsuo Deguchi , Chihiro Matsui

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

In this paper, we show the integrability of spin-1/2 XXZ Heisenberg chain with two arbitrary spin boundary Impurities. By using the fusion method, we generalize it to the spin-1 XXZ chain. Then the eigenvalues of Hamiltonians of these…

Condensed Matter · Physics 2009-10-31 Boyu Hou , Kangjie Shi , Ruihong Yue , Shaoyou Zhao

The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are…

Mathematical Physics · Physics 2015-06-18 Xin Zhang , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We formulate the algebraic Bethe ansatz solution of the SU(N) vertex models with rather general non-diagonal toroidal boundary conditions. The reference states needed in the Bethe ansatz construction are found by performing gauge…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 G. A. P. Ribeiro , M. J. Martins , W. Galleas