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The Bethe ansatz for the one-dimensional s=1/2 Heisenberg ferromagnet is introduced at an elementary level. The presentation follows Bethe's original work very closely. A detailed description and a complete classification of all two-magnon…

Statistical Mechanics · Physics 2007-05-23 Michael Karbach , Gerhard Muller

We use the Bethe-Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice…

Statistical Mechanics · Physics 2016-10-04 Leticia F. Cugliandolo , Giuseppe Gonnella , Alessandro Pelizzola

We solve the gl(1|2) generalized model by means of the algebraic Bethe ansatz. The resulting eigenvalue of the transfer matrix and the Bethe ansatz equations depend on three complex functions, called the parameters of the generalized model.…

Statistical Mechanics · Physics 2009-11-07 Frank Göhmann

We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider…

High Energy Physics - Theory · Physics 2008-11-26 Rajan Murgan

The exactly solvable four-vertex model on a square grid with the different boundary conditions is considered. The application of the Algebraic Bethe Ansatz method allows to calculate the partition function of the model. For the fixed…

Statistical Mechanics · Physics 2009-11-13 N. M. Bogoliubov

We show that the Bethe vectors are non-zero vectors in the sl_{r+1} Gaudin model. Moreover, we show that the norm of a Bethe vector is equal to the Hessian of the corresponding master function at the corresponding non-degenerate critical…

Quantum Algebra · Mathematics 2007-05-23 Evgeny Mukhin , Alexander Varchenko

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression…

Mathematical Physics · Physics 2014-10-23 N. Cirilo António , N. Manojlović , I. Salom

We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin…

Mathematical Physics · Physics 2009-09-25 N. Kitanine , K. K. Kozlowski , J. M. Maillet , N. A. Slavnov , V. Terras

A wide class of problems in combinatorics, computer science and physics can be described along the following lines. There are a large number of variables ranging over a finite domain that interact through constraints that each bind a few…

Probability · Mathematics 2017-11-17 Victor Bapst , Amin Coja-Oghlan

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

A Bethe Ansatz solution of the open spin-1/2 XXZ quantum spin chain with nondiagonal boundary terms has recently been proposed. Using a numerical procedure developed by McCoy et al., we find significant evidence that this solution can yield…

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

We apply the nested algebraic Bethe ansatz to a model of one-dimensional two-component Bose gas with delta-function repulsive interaction. Using a lattice approximation of the L-operator we find Bethe vectors of the model in the continuous…

Mathematical Physics · Physics 2015-02-25 N. A. Slavnov

This article gives a pedagogic derivation of the Bethe Ansatz solution for 1D interacting anyons. This includes a demonstration of the subtle role of the anyonic phases in the Bethe Ansatz arising from the anyonic commutation relations. The…

Statistical Mechanics · Physics 2007-05-23 M. T. Batchelor , X. -W. Guan , J. -S. He

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 show that a system consisting of two interacting particles with mass ratio $3$ or $1/3$ in a hard-wall box can be exactly solved by using Bethe-type ansatz. The ansatz is based on a finite superposition of plane waves associated with a…

Quantum Physics · Physics 2019-12-11 Yanxia Liu , Fan Qi , Yunbo Zhang , Shu Chen

The structure of Bethe vectors for generalised models associated with the XXX- and XXZ-type R-matrix is investigated. The Bethe vectors in terms of two--component and multi--component models are described. Consequently, their structure in…

Mathematical Physics · Physics 2017-08-02 J. Fuksa

Thermodynamic Bethe ansatz equations are coupled non-linear integral equations which appear frequently when solving integrable models. Those associated with models with N=2 supersymmetry can be related to differential equations, among them…

High Energy Physics - Theory · Physics 2007-05-23 Paul Fendley

Recently it was shown that the eigenfunctions for the the asymmetric exclusion problem and several of its generalizations as well as a huge family of quantum chains, like the anisotropic Heisenberg model, Fateev- Zamolodchikov model,…

Statistical Mechanics · Physics 2007-05-23 Matheus Jatkoske Lazo

We analyze the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process on a finite lattice and with the most general open boundary conditions. We extend results obtained…

Statistical Mechanics · Physics 2009-01-27 Jan de Gier , Fabian H L Essler

The Bethe ansatz equation is solved to obtain analytically the leading finite-size correction of the spectra of the asymmetric XXZ chain and the accompanying isotropic 6-vertex model near the antiferromagnetic phase boundary at zero…

Statistical Mechanics · Physics 2009-10-28 Doochul Kim