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Related papers: Bethe Equations "on the Wrong Side of Equator"

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A general fusion method to find solutions to the reflection equation in higher spin representations starting from the fundamental one is shown. The method is illustrated by applying it to obtaining the $K$ diagonal boundary matrices in an…

High Energy Physics - Theory · Physics 2009-10-28 Julio Abad , Miguel Rios

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

We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(\fn)), Y(gl(\fm|\fn)), U_{q}(gl(\fn)) or U_{q}(gl(\fm|\fn)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of…

Mathematical Physics · Physics 2015-05-13 S. Belliard , E. Ragoucy

We continue to study the excited states for the XXZ- spin chain corresponding to the complex roots of the Bethe Ansatz equations with the imaginary part equal to $\pi/2$. We propose the particle-hole symmetry which relates the eigenstates…

Mathematical Physics · Physics 2015-06-15 A. A. Ovchinnikov

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

Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, a systematic method for retrieving the Bethe-type eigenstates of integrable models without obvious reference state is developed by employing certain…

Mathematical Physics · Physics 2015-07-16 Xin Zhang , Yuan-Yuan Li , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

In this paper we propose a simple method for building exactly solvable multi-parameter spectral equations which in turn can be used for constructing completely integrable and exactly solvable quantum systems. The method is based on the use…

High Energy Physics - Theory · Physics 2007-05-23 Dieter Mayer , Alexander Ushveridze , Zbigniew Walczak

Q-systems provide an efficient way of solving Bethe equations. We formulate here Q-systems for both the isotropic and anisotropic open Heisenberg quantum spin-1/2 chains with diagonal boundary magnetic fields. We check these Q-systems using…

High Energy Physics - Theory · Physics 2020-08-26 Rafael I. Nepomechie

A non homogeneous spin chain in the representations $ \{3 \}$ and $ \{3^*\}$ of $A_2$ is analyzed. We find that the naive nested Bethe ansatz is not applicable to this case. A method inspired in the nested Bethe ansatz, that can be applied…

High Energy Physics - Theory · Physics 2009-10-30 Julio Abad , Miguel Rios

The solution of Bethe ansatz equations for XXZ spin chain with the parameter $q$ being a root of unity is infamously subtle. In this work, we develop the rational $Q$-system for this case, which offers a systematic way to find all physical…

High Energy Physics - Theory · Physics 2024-05-29 Jue Hou , Yunfeng Jiang , Yuan Miao

The trigonometric su(n) spin chain with anti-periodic boundary condition (su(n) spin torus) is demonstrated to be Yang-Baxter integrable. Based on some intrinsic properties of the R-matrix, certain operator product identities of the…

Mathematical Physics · Physics 2016-08-18 Kun Hao , Junpeng Cao , Guang-Liang Li , Wen-Li Yang , Kangjie Shi , Yupeng Wang

Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of mathematical physics, algebra and combinatorics. Such a solution consists of a set $X$ and a function r:X x X --> X x X which satisfies the braid relation. We…

Quantum Algebra · Mathematics 2009-07-27 Tatiana Gateva-Ivanova , Peter Cameron

Using algebraic Bethe ansatz and the solution of the quantum inverse scattering problem, we compute compact representations of the spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field. At lattice distance m,…

High Energy Physics - Theory · Physics 2011-07-19 N. Kitanine , J. M. Maillet , N. A. Slavnov , V. Terras

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

Two branches of integrable open quantum-group invariant $D_{n+1}^{(2)}$ quantum spin chains are known. For one branch (epsilon=0), a complete Bethe ansatz solution has been proposed. However, the other branch (epsilon=1) has so far resisted…

High Energy Physics - Theory · Physics 2020-01-08 Rafael I. Nepomechie , Rodrigo A. Pimenta , Ana L. Retore

Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) $J$ are derived based on the Jordan-Schwinger (differential) boson realization of the $SU(2)$ algebra after desired Euler rotations, where…

Quantum Physics · Physics 2017-02-09 Feng Pan , Yao-Zhong Zhang , Jerry P. Draayer

We consider the open spin-s XXZ quantum spin chain with N sites and general integrable boundary terms for generic values of the bulk anisotropy parameter, and for values of the boundary parameters which satisfy a certain constraint. We…

Mathematical Physics · Physics 2010-04-08 Luc Frappat , Rafael Nepomechie , Eric Ragoucy

The U_q(\hat{sl}(2)) Bethe equation is studied at q=0. A linear congruence equation is proposed related to the string solutions. The number of its off-diagonal solutions is expressed in terms of an explicit combinatorial formula and…

Quantum Algebra · Mathematics 2007-05-23 Atsuo Kuniba , Tomoki Nakanishi

We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded…

Mathematical Physics · Physics 2015-05-20 Rouven Frassek , Tomasz Lukowski , Carlo Meneghelli , Matthias Staudacher

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