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Related papers: Modified Algebraic Bethe Ansatz: Twisted XXX Case

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We consider the sl(N) twisted Yangian quantum spin chain. In particular, we study the bulk and boundary scattering of the model via the solution of the Bethe ansatz equations in the thermodynamic limit. Local defects are also implemented in…

Mathematical Physics · Physics 2015-05-22 Jean Avan , Anastasia Doikou , Nikos Karaiskos

We discover a family of local deformations that leave part of the spectrum intact for strongly interacting and exactly solvable quantum many-body systems. Since the deformation preserves the Bethe Ansatz equations (BAE), it is dubbed the…

Statistical Mechanics · Physics 2024-10-15 Yunfeng Jiang , Yuan Miao

We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from…

Mathematical Physics · Physics 2024-06-12 Allan John Gerrard

We present the exact solution of a family of two-spins models. The models are solved by the algebraic Bethe ansatz method using the $gl(2)$-invariant $R$-matrix and a multi-spins Lax operator. The interactions are by the Heisenberg spins…

Mathematical Physics · Physics 2019-09-18 G. Santos

We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin-1/2 Heisenberg chains using the algebraic Bethe ansatz. In this representation, the components of the Bethe eigenstates are expressed as traces of…

Statistical Mechanics · Physics 2014-11-20 Hosho Katsura , Isao Maruyama

We propose that the Baxter's $Q$-operator for the XYZ quantum spin chain with open boundary conditions is given by the $j\to \infty$ limit of the corresponding transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. The…

High Energy Physics - Theory · Physics 2010-04-05 Wen-Li Yang , Yao-Zhong Zhang

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

We study the equations for the quasi-momenta which characterize the wave-functions in the Bethe ansatz for the XXX-Heisenberg model. We show in a simple analytical fashion, that the usual ``string hypothesis" incorrectly predicts the number…

High Energy Physics - Theory · Physics 2009-10-22 K. Isler , M. B. Paranjape

We investigate symmetry properties of the Bethe ansatz wave functions for the Heisenberg $XXZ$ spin chain. The $XXZ$ Hamiltonian commutes simultaneously with the shift operator $T$ and the lattice inversion operator $V$ in the space of…

Statistical Mechanics · Physics 2009-10-31 Jae Dong Noh , Deok-Sun Lee , Doochul Kim

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading…

Strongly Correlated Electrons · Physics 2009-11-07 A. Foerster , M. D. Gould , X. -W. Guan , I. Roditi , H. -Q Zhou

We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang-Baxter algebra. The main deviation from the standard approach consists in a half infinite 'Sklyanin lattice' made of the eigenvalues of…

Mathematical Physics · Physics 2014-11-21 Luigi Amico , Holger Frahm , Andreas Osterloh , Tobias Wirth

A systematic perturbation theory is developed for the ESR shift and is applied to the spin-1/2 Heisenberg chain. Using the Bethe ansatz technique, we exactly analyze the resonance shift in the first order of perturbative expansion with…

Statistical Mechanics · Physics 2009-11-11 Y. Maeda , K. Sakai , M. Oshikawa

An inhomogeneous T-Q equation has recently been proposed by Cao, Yang, Shi and Wang for the open spin-1/2 XXX chain with general (nondiagonal) boundary terms. We argue that a simplified version of this equation describes all the eigenvalues…

Mathematical Physics · Physics 2015-06-16 Rafael I. Nepomechie

A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to…

Mathematical Physics · Physics 2024-12-18 Guang-Liang Li , Junpeng Cao , Pei Sun , Wen-Li Yang , Kangjie Shi , Yupeng Wang

Using the XXX Heisenberg chain as an example, based on the symmetry properties of the eigenstates with respect to reversing all the spins we argue, that the basic SU(2) symmetry of the model is inherited by the excitations with slight…

Condensed Matter · Physics 2007-05-23 F. Woynarovich

It was recently shown that the string theory duals of certain deformations of the N=4 gauge theory can be obtained by a combination of T-duality transformations and coordinate shifts. Here we work out the corresponding procedure of twisting…

High Energy Physics - Theory · Physics 2011-03-23 N. Beisert , R. Roiban

We compute the eigenfunctions and eigenvalues of the periodic integrable spin s XXX model using the coordinate Bethe ansatz. To do so, we compute explicitly the Hamiltonian of the model. These results generalize what has been obtained for…

Mathematical Physics · Physics 2011-01-13 Nicolas Crampé , Eric Ragoucy , Ludovic Alonzi

We investigate special solutions to the Bethe Ansatz equations (BAE) for open integrable $XXZ$ Heisenberg spin chains containing phantom (infinite) Bethe roots. The phantom Bethe roots do not contribute to the energy of the Bethe state, so…

Statistical Mechanics · Physics 2021-03-24 Xin Zhang , Andreas Klümper , Vladislav Popkov

We construct the coordinate Bethe ansatz for all eigenstates of the open spin-$\frac12$ XXZ chain that fulfill the phantom roots criterion (PRC). Under the PRC, the Hilbert space splits into two invariant subspaces and there are two sets of…

Statistical Mechanics · Physics 2022-02-01 Xin Zhang , Andreas Kluemper , Vladislav Popkov

In this paper we propose a method based on the algebraic Bethe ansatz leading to explicit results for the form factors of quantum spin chains in the thermodynamic limit. Starting from the determinant representations we retrieve in…

Mathematical Physics · Physics 2019-06-26 Nikolai Kitanine , Giridhar Kulkarni