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Related papers: On the structure of Bethe vectors

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It is shown that solutions of the Bethe ansatz equations for the inhomogeneous arbitrary spin XXX or XXZ model satisfy certain identites which generalize those, recently obtained by K.Fabricius and B.M.McCoy, for solutions of the Bethe…

Mathematical Physics · Physics 2007-05-23 V. Tarasov

Several studies have exploited the integrable structure of central spin models to deepen understanding of these fundamental systems. In recent years, an underlying supersymmetry for systems with XX interactions has been uncovered. Here we…

Exactly Solvable and Integrable Systems · Physics 2023-04-03 W J P van Tonder , J Links

The Bethe ansatz, both in its coordinate and its algebraic version, is an exceptional method to compute the eigenvectors and eigenvalues of integrable systems. However, computing correlation functions using the eigenvectors thus constructed…

High Energy Physics - Theory · Physics 2023-12-25 Rafael Hernandez , Juan Miguel Nieto

The Bethe ansatz equations for the spin 1/2 Heisenberg XXZ spin chain are numerically solved, and the energy eigenvalues are determined for the anti-ferromagnetic case. We examine the relation between the XXZ spin chain and the Thirring…

High Energy Physics - Theory · Physics 2009-11-10 T. Fujita , T. Kobayashi , M. Hiramoto , H. Takahashi

We consider correlation functions of the spin-$\half$ XXX and XXZ Heisenberg chains in a magnetic field. Starting from the algebraic Bethe Ansatz we derive representations for various correlation functions in terms of determinants of…

High Energy Physics - Theory · Physics 2009-10-28 F. H. L. Essler , H. Frahm , A. G. Izergin , V. E. Korepin

We briefly review Bethe Ansatz solutions of the integrable open spin-1/2 XXZ quantum spin chain derived from functional relations obeyed by the transfer matrix at roots of unity.

High Energy Physics - Theory · Physics 2007-05-23 Rafael I. Nepomechie

We consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 C. S. Melo , G. A. P. Ribeiro , M. J. Martins

The one-dimensional Heisenberg XXX spin chain appears in a special limit of the AdS/CFT integrable system. We review various ways of proving its integrability, and discuss the associated methods of solution. In particular, we outline the…

High Energy Physics - Theory · Physics 2015-05-20 Matthias Staudacher

In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in the framework of the quantum inverse scattering method. Following the algebraic Bethe ansatz we diagonalise the introduced…

Mathematical Physics · Physics 2023-01-04 Rouven Frassek , István M. Szécsényi

A chiral coordinate Bethe ansatz method is developed to study the periodic XYZ chain. We construct a set of chiral vectors with fixed number of kinks. All vectors are factorized and have simple structures. Under roots of unity conditions,…

Statistical Mechanics · Physics 2024-03-21 Xin Zhang , Andreas Klümper , Vladislav Popkov

Using the algebraic Bethe ansatz, we derive a matrix product representation of the exact Bethe-ansatz states of the six-vertex Heisenberg chain (either XXX or XXZ and spin-$\frac{1}{2}$) with open boundary conditions. In this…

Quantum Physics · Physics 2017-07-14 Zhongtao Mei , C. J. Bolech

The eigenvectors of the Hamiltionians of the XYZ Gaudin model are constructed by means of the algebraic Bethe Ansatz. The construction is based on the quasi-classical limit of the corresponding results for the inhomogeneous higher spin…

q-alg · Mathematics 2009-10-30 E. K. Sklyanin , T. Takebe

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

We show that the Shapovalov norm of a Bethe vector in the Gaudin model is equal to the Hessian of the logarithm of the corresponding master function at the corresponding isolated critical point. We show that different Bethe vectors are…

Quantum Algebra · Mathematics 2007-05-23 Alexander Varchenko

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 novel determinantal representation for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s=1/2 XXZ model is used to calculate transition rates for dynamic spin structure factors in the planar…

Strongly Correlated Electrons · Physics 2009-11-10 Daniel Biegel , Michael Karbach , Gerhard Mueller

We provide a conjecture for the following two quantities related with the spin-$\frac{1}{2}$ isotropic Heisenberg model defined over rings of even lengths: (i) the number of the solutions to the Bethe ansatz equations which correspond to…

Mathematical Physics · Physics 2014-05-08 Anatol N. Kirillov , Reiho Sakamoto

We consider the XXZ spin chain with diagonal boundary conditions in the framework of algebraic Bethe Ansatz. Using the explicit computation of the scalar products of Bethe states and a revisited version of the bulk inverse problem, we…

High Energy Physics - Theory · Physics 2008-11-26 N. Kitanine , K. K. Kozlowski , J. M. Maillet , G. Niccoli , N. A. Slavnov , V. Terras

A generalization of the eight vertex model by means of higher spin representations of the Sklyanin algebra is investigated by the quantum inverse scattering method and the algebraic Bethe Ansatz. Under the well-known string hypothesis…

q-alg · Mathematics 2009-10-28 Takashi Takebe

We present a generalization of the coordinate Bethe ansatz that allows us to solve integrable open XXZ and ASEP models with non-diagonal boundary matrices, provided their parameters obey some relations. These relations extend the ones…

Statistical Mechanics · Physics 2011-03-07 Nicolas Crampé , Eric Ragoucy , Damien Simon