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Related papers: The Algebraic Bethe Ansatz and Tensor Networks

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In this paper, the algebraic Bethe ansatz with periodic boundary conditions is used to investigate trigonometric vertex models associated with the fundamental representations of the non-exceptional Lie algebras. This formulation allow us to…

Exactly Solvable and Integrable Systems · Physics 2011-02-16 A. Lima-Santos

Recently, the XXX spin chain with arbitrary boundary fields was successfully solved [1] via the off-diagonal Bethe ansatz method [2]. The correctness and the completeness of this solution were numerically verified by Nepomechie for one…

Statistical Mechanics · Physics 2013-09-26 Yuzhu Jiang , Shuai Cui , Junpeng Cao , Wen-Li Yang , Yupeng Wang

I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated more superficially, only the specific…

High Energy Physics - Theory · Physics 2007-05-23 L. D. Faddeev

We diagonalize Q-operators for rational homogeneous sl(2)-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang-Baxter equation we…

Mathematical Physics · Physics 2017-11-28 Rouven Frassek

Every solution of the Bethe-ansatz equations (BAE) is characterized by a set of quantum numbers, by which we can evaluate it numerically. However, no general rule is known how to give quantum numbers for the physical solutions of BAE. For…

Statistical Mechanics · Physics 2016-04-20 Tetsuo Deguchi , Pulak Ranjan Giri

We present a nested algebraic Bethe ansatz for one-dimensional open so(2n)- and sp(2n)-symmetric spin chains with diagonal boundary conditions and described by the extended twisted Yangian. We use a generalization of the Bethe ansatz…

Mathematical Physics · Physics 2020-02-19 Allan Gerrard , Vidas Regelskis

We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of…

Mathematical Physics · Physics 2013-11-20 Wenrui Hao , Rafael I. Nepomechie , Andrew J. Sommese

We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we derive a generalized form of T-Q relation involving more than one independent Q(u), which…

Mathematical Physics · Physics 2015-06-05 Rashad Baiyasi , Rajan Murgan

We investigate integrable boundary states in the anisotropic Heisenberg chain under periodic or twisted boundary conditions, for both even and odd system lengths. Our work demonstrates that the concept of integrable boundary states can be…

High Energy Physics - Theory · Physics 2026-01-26 Xin Qian , Xin Zhang

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

The transfer matrix of the XXZ open spin-1/2 chain with general integrable boundary conditions and generic anisotropy parameter (q is not a root of unity and |q|=1) is diagonalized using the representation theory of the q-Onsager algebra.…

High Energy Physics - Theory · Physics 2015-06-26 P. Baseilhac , K. Koizumi

We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz…

High Energy Physics - Theory · Physics 2014-11-18 Luca Mezincescu , Rafael I. Nepomechie

Determinant representations of form factors are used to represent the spontaneous magnetization of the Heisenberg XXZ chain (Delta >1) on the finite lattice as the ratio of two determinants. In the thermodynamic limit (the lattice of…

solv-int · Physics 2018-08-30 A. G. Izergin , N. Kitanine , J. M. Maillet , V. Terras

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

The properties of the most probable ground state candidate for the XXZ spin chain with the anisotropy parameter equal to -1/2 and an odd number of sites is considered. Some linear combinations of the components of the considered state,…

Mathematical Physics · Physics 2007-05-23 A. V. Razumov , Yu. G. Stroganov

As part of a study that investigates the dynamics of the s=1/2 XXZ model in the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz equations for the case Delta=0 (XX model). We identify the general structure of the…

Strongly Correlated Electrons · Physics 2009-11-10 Daniel Biegel , Michael Karbach , Gerhard Muller , Klaus Wiele

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 compute the finite size spectrum for the spin 1/2 XXZ chain with twisted boundary conditions, for anisotropy in the regime $0< \gamma <\pi/2$, and arbitrary twist $\theta$. The string hypothesis is employed for treating complex…

High Energy Physics - Theory · Physics 2008-11-26 T. Nassar , O. Tirkkonen

We introduce a generalization of the original Coordinate Bethe Ansatz that allows to treat the case of open spin chains with non-diagonal boundary matrices. We illustrate it on two cases: the XXX and XXZ chains. Short review on a joint work…

High Energy Physics - Theory · Physics 2015-05-30 E. Ragoucy

We express $D^{(2)}_{2}$ transfer matrices as products of $A^{(1)}_{1}$ transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz.…

High Energy Physics - Theory · Physics 2021-01-20 Rafael I. Nepomechie , Ana L. Retore