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Related papers: Bethe Ansatze for 19-vertex Models

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In this paper, we consider the parameterization of the spectra of the three-state critical Potts quantum chain with integrable twisted boundary conditions in terms of Bethe ansatz type equations. The Bethe equations are found by…

Mathematical Physics · Physics 2026-02-23 M. J. Martins

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

This work is concerned with the quasi-classical limit of the boundary quantum inverse scattering method for the $osp(1|2)$ vertex model with diagonal $K$-matrices. In this limit Gaudin's Hamiltonians with boundary terms are presented and…

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

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

We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an…

Mathematical Physics · Physics 2009-11-11 D. Arnaudon , N. Crampe , A. Doikou , L. Frappat , E. Ragoucy

The generic quantum $\tau_2$-model (also known as Baxter-Bazhanov-Stroganov (BBS) model) with periodic boundary condition is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix (solutions…

Mathematical Physics · Physics 2015-11-04 Xiaotian Xu , Junpeng Cao , Shuai Cui , Wen-Li Yang , Kangjie Shi , Yupeng Wang

The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su(n)-invariant spin chain model with both periodic and…

High Energy Physics - Theory · Physics 2015-06-18 Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

The quantum $\tau_2$-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an…

Mathematical Physics · Physics 2016-12-21 Xiaotian Xu , Kun Hao , Tao Yang , Junpeng Cao , Wen-Li Yang , Kangjie Shi

Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin-1/2 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge…

Mathematical Physics · Physics 2015-05-20 Xin Zhang , Yuan-Yuan Li , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We consider the case of an integrable quantum spin chain with ``soliton non-preserving'' boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer…

High Energy Physics - Theory · Physics 2007-05-23 Anastasia Doikou

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

We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a…

Mathematical Physics · Physics 2011-02-16 Daniel Arnaudon , Nicolas Crampe , Anastasia Doikou , Luc Frappat , Eric Ragoucy

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

We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the…

Statistical Mechanics · Physics 2007-05-23 Jan de Gier , Fabian H. L. Essler

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

The thermodynamic Bethe ansatz is applied to a quantum integrable spin chain associated with the Lie superalgebra osp(1|2). Using the string hypothesis, we derive a set of infinite number of non-linear integral equations (thermodynamic…

Mathematical Physics · Physics 2009-10-31 Kazumitsu Sakai , Zengo Tsuboi

We propose a new approach to the spinor-spinor R-matrix with orthogonal and symplectic symmetry. Based on this approach and the fusion method we relate the spinor-vector and vector-vector monodromy matrices for quantum spin chains. We…

Mathematical Physics · Physics 2020-04-22 D. Karakhanyan , R. Kirschner

A quantum algebra invariant integrable closed spin 1 chain is introduced and analysed in detail. The Bethe ansatz equations as well as the energy eigenvalues of the model are obtained. The highest weight property of the Bethe vectors with…

solv-int · Physics 2015-06-26 Jon Links , Angela Foerster , Michael Karowski

In this text, we provide a detailed exposition of the Algebraic Bethe ansatz for square ice (or six vertex model), which allows the construction of candidate eigenvectors for the transfer matrices of this model. We also prove some formula…

Statistical Mechanics · Physics 2019-04-30 Silvère Gangloff

The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe…

Mathematical Physics · Physics 2015-07-02 C. Burdik , J. Fuksa , A. P. Isaev , S. O. Krivonos , O. Navratil