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Related papers: The Algebraic Bethe Ansatz and Tensor Networks

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We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N = (2,2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz. We construct the wave functions of off-shell Bethe states as…

High Energy Physics - Theory · Physics 2017-12-06 Mathew Bullimore , Hee-Cheol Kim , Tomasz Lukowski

A recently proposed strongly correlated electron system associated with the Temperley-Lieb algebra is solved by means of the coordinate Bethe ansatz for periodic and closed boundary conditions.

solv-int · Physics 2009-10-31 A. Lima-Santos , I. Roditi , A. Foerster

The Bethe ansatz solutions for an open XXZ spin chain with arbitrary spin with N sites and nondiagonal boundary terms are revisited. The anisotropy parameter, for cases considered here, has values \eta = i \pi r/q, where r and q are…

Mathematical Physics · Physics 2015-06-19 Rajan Murgan , Christopher Silverthorn

Every solution of the Bethe ansatz equations (BAE) is characterized by a set of quantum numbers called the Bethe quantum numbers, which are fundamental for evaluating it numerically. We rigorously derive the Bethe quantum numbers for the…

Mathematical Physics · Physics 2024-09-10 Takashi Imoto , Tetsuo Deguchi

We develop the technique of Thermodynamic Bethe Ansatz to investigate the ground state and the spectrum in the thermodynamic limit of the staggered $XXZ$ models proposed recently as an example of integrable ladder model. This model appeared…

High Energy Physics - Theory · Physics 2007-05-23 V. V. Mkhitaryan , A. G. Sedrakyan

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 construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the theory are played by a particular infinite-dimensional…

Mathematical Physics · Physics 2020-10-13 Bart Vlaar , Robert Weston

We have recently proposed a Bethe Ansatz solution of the open spin-1/2 XXZ quantum spin chain with general integrable boundary terms (containing six free boundary parameters) at roots of unity. We use this solution, together with an…

High Energy Physics - Theory · Physics 2010-10-27 Rajan Murgan , Rafael I. Nepomechie , Chi Shi

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

In in a nutshell, the classical geometric $q$-Langlands duality can be viewed as a correspondence between the space of $(G,q)$-opers and the space of solutions of $^L\mathfrak{g}$ XXZ Bethe Ansatz equations. The latter describe spectra of…

Algebraic Geometry · Mathematics 2026-04-06 Peter Koroteev , Myungbo Shim , Rahul Singh

The $sl_q(2)$-quantum group invariant spin 1/2 XXZ-Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for $q$ equal to a root of unity possess a finite number of…

High Energy Physics - Theory · Physics 2010-11-01 G. Juettner , M. Karowski

Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair…

Quantum Physics · Physics 2021-05-26 Matthias Christandl , Fulvio Gesmundo , Daniel Stilck Franca , Albert H. Werner

We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the…

Statistical Mechanics · Physics 2007-05-23 Jan de Gier , Fabian H. L. Essler

Stationary probability distributions for stochastic processes on linear chains with closed or open ends are obtained using the matrix product Ansatz. The matrices are representations of some quadratic algebras. The algebras and the types of…

Statistical Mechanics · Physics 2009-10-30 F. C. Alcaraz , S. Dasmahapatra , V. Rittenberg

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

Bethe ansatz equations for spin-$s$ Heisenberg spin chain with $s\ge1$ are significantly more difficult to analyze than the spin-$\tfrac{1}{2}$ case, due to the presence of repeated roots. As a result, it is challenging to derive extra…

High Energy Physics - Theory · Physics 2024-05-01 Jue Hou , Yunfeng Jiang , Rui-Dong Zhu

In this paper we study the spectrum of the spin-1 Temperley-Lieb spin chain with integrable open boundary conditions. We obtain the eigenvalue expressions as well as its associated Bethe ansatz equations by means of the coordinate Bethe…

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

We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon…

High Energy Physics - Theory · Physics 2016-09-06 C. M. Yung , M. T. Batchelor

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 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