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Related papers: Algebraic Bethe ansatz for U(1) Invariant Integrab…

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In this work we demonstrate how one can, in a generic approach, derive a set of $N$ simple quadratic Bethe equations for integrable Richardson-Gaudin (RG) models built out of $N$ spins-1/2. These equations depend only on the $N$ eigenvalues…

Mathematical Physics · Physics 2018-08-01 Claude Dimo , Alexandre Faribault

We consider the Temperley-Lieb (TL) open quantum spin chain with "free" boundary conditions associated with the spin-$s$ representation of quantum-deformed $sl(2)$. We construct the transfer matrix, and determine its eigenvalues and the…

Mathematical Physics · Physics 2016-10-04 Rafael I. Nepomechie , Rodrigo A. Pimenta

We derive the Bethe Ansatz Equations on the half line for particles interacting through factorized $S$-matrices invariant relative to the centrally extended $su(2|2)$ Lie superalgebra and $su(1|2)$ open boundaries. These equations may be of…

High Energy Physics - Theory · Physics 2009-08-03 W. Galleas

We propose a novel quantum integrable model for every non-simply laced simple Lie algebra ${\mathfrak g}$, which we call the folded integrable model. Its spectra correspond to solutions of the Bethe Ansatz equations obtained by folding the…

Quantum Algebra · Mathematics 2024-10-30 Edward Frenkel , David Hernandez , Nicolai Reshetikhin

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 J. Links , H. -Q. Zhou , R. H. McKenzie , M. D. Gould

We consider the integrable open XX quantum spin chain with nondiagonal boundary terms. We derive an exact inversion identity, using which we obtain the eigenvalues of the transfer matrix and the Bethe Ansatz equations. For generic values of…

High Energy Physics - Theory · Physics 2008-11-26 Rafael I. Nepomechie

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

An integrable version of the supersymmetric t-J model which is quantum group invariant as well as periodic is introduced and analysed in detail. The model is solved through the algebraic nested Bethe ansatz method.

Statistical Mechanics · Physics 2009-10-30 Angela Foerster

We derive exactly scalar products and form factors for integrable higher-spin XXZ chains through the algebraic Bethe-ansatz method. Here spin values are arbitrary and different spins can be mixed. We show the affine quantum-group symmetry,…

Statistical Mechanics · Physics 2011-07-06 Tetsuo Deguchi , Chihiro Matsui

We investigate the algebraic structure of a recently proposed integrable $t-J$ model with impurities. Three forms of the Bethe ansatz equations are presented corresponding to the three choices for the grading. We prove that the Bethe ansatz…

Condensed Matter · Physics 2009-10-31 Angela Foerster , Jon Links , Arlei Prestes Tonel

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

The Gaudin model based on the sl_2-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a…

Exactly Solvable and Integrable Systems · Physics 2015-05-18 N. Cirilo-Antonio , N. Manojlovic , A. Stolin

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 derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The…

High Energy Physics - Theory · Physics 2023-07-18 Dmitry Chernyak , Azat M. Gainutdinov , Jesper Lykke Jacobsen , Hubert Saleur

The Bethe ansatz equations of the fundamental Sp(2N) integrable model are solved by a peculiar configuration of roots leading us to determine the nature of the excitations. They consist of N elementary generalized spinons and N-1 composite…

Statistical Mechanics · Physics 2016-08-31 M. J. Martins

The nineteen-vertex models of Zamolodchikov-Fateev, Izergin-Korepin and the supersymmetric osp(1|2) with periodic boundary conditions are studied. We find the spectrum of these quantum spin chains using the Coordinate Bethe Ansatz. The…

High Energy Physics - Theory · Physics 2010-04-08 A. Lima-Santos

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 apply the thermodynamic Bethe Ansatz to investigate the high energy behaviour of a class of scattering matrices which have recently been proposed to describe the Homogeneous sine-Gordon models related to simply laced Lie algebras. A…

High Energy Physics - Theory · Physics 2014-11-18 O. A. Castro-Alvaredo , A. Fring , C. Korff , J. L. Miramontes

We present a method to construct a basis of singular and non-singular common eigenvectors for Gaudin Hamiltonians in a tensor product module of the Lie algebra SL(2). The subset of singular vectors is completely described by analogy with…

Mathematical Physics · Physics 2009-11-07 Daniela Garajeu , Annamaria Kiss

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