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Related papers: The Bethe Ansatz Equations for Reflecting Magnons

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In these lectures the introduction to algebraic aspects of Bethe Ansatz is given. The applications to the seminal spin 1/2 XXX model is discussed in detail and the generalization to higher spin as well as XXZ and lattice Sine-Gordon model…

High Energy Physics - Theory · Physics 2015-06-26 L. D. Faddeev

We use the algebraic Bethe ansatz to obtain the eigenvalues and eigenvectors of the spin-1 Temperley-Lieb open quantum chain with "free" boundary conditions. We exploit the associated reflection algebra in order to prove the off-shell…

Mathematical Physics · Physics 2016-10-04 Rafael I. Nepomechie , Rodrigo A. Pimenta

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 procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov-Fateev and Izergin-Korepin,…

Exactly Solvable and Integrable Systems · Physics 2014-11-18 E. C. Fireman , A. Lima-Santos , W. Utiel

The anisotropic spin-1/2 chains with arbitrary boundary fields are diagonalized with the off-diagonal Bethe ansatz method. Based on the properties of the R-matrix and the K-matrices, an operator product identity of the transfer matrix is…

Statistical Mechanics · Physics 2015-06-16 Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

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

Based on the inhomogeneous T-Q relation and the associated Bethe Ansatz equations obtained via the off-diagonal Bethe Ansatz, we construct the Bethe-type eigenstates of the SU(2)-invariant spin-s chain with generic non-diagonal boundaries…

Mathematical Physics · Physics 2016-08-18 Lijun Yang , Xin Zhang , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

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 consider the N-site U_{q}(gl(N)) integrable spin chain with periodic and open diagonal soliton-preserving boundary conditions. By employing analytical Bethe ansatz techniques we are able to determine the spectrum and the corresponding…

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

The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant…

High Energy Physics - Theory · Physics 2009-10-22 H. J. de Vega , A. González--Ruiz

We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N = (2,2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz. We construct the wave functions of off-shell Bethe states as…

High Energy Physics - Theory · Physics 2017-12-06 Mathew Bullimore , Hee-Cheol Kim , Tomasz Lukowski

Using the algebraic Bethe ansatz, we derive a matrix product representation of the exact Bethe-ansatz states of the six-vertex Heisenberg chain (either XXX or XXZ and spin-$\frac{1}{2}$) with open boundary conditions. In this…

Quantum Physics · Physics 2017-07-14 Zhongtao Mei , C. J. Bolech

We define one-dimensional particles as non-abelian representations of the symmetric group $S_N$. The exact solution of an $XXZ$ type Hamiltonian built up with such particles is achieved using the coordinate Bethe Ansatz. The Bethe equations…

Strongly Correlated Electrons · Physics 2007-05-23 Luigi Amico , Andreas Osterloh , Ulrich Eckern

We present in an unified and detailed way the Nested Bethe Ansatz for closed spin chains based on Y(gl(n)), Y(gl(m|n)), U_q(gl(n)) or U_q(gl(m|n)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain. In…

Mathematical Physics · Physics 2010-04-07 S. Belliard , E. Ragoucy

We continue the survey initiated in arXiv:2012.14197 to explore the Bethe/Gauge correspondence between supersymmetric SO/Sp gauge theories in 2d/3d/4d and open spin chain with integrable boundaries. We collect the known Bethe ansatz…

High Energy Physics - Theory · Physics 2024-10-01 Ziwei Wang , Rui-Dong Zhu

This work is concerned with the formulation of the graded quantum inverse scattering method for a class oflattice models with reflecting boundary conditions. The $sl(2|1)^{(2)}$ and $osp(2|1)$ models are considered with their diagonal…

Exactly Solvable and Integrable Systems · Physics 2010-04-08 V. Kurak , A. Lima-Santos

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

In in a nutshell, the classical geometric $q$-Langlands duality can be viewed as a correspondence between the space of $(G,q)$-opers and the space of solutions of $^L\mathfrak{g}$ XXZ Bethe Ansatz equations. The latter describe spectra of…

Algebraic Geometry · Mathematics 2026-04-06 Peter Koroteev , Myungbo Shim , Rahul Singh

We obtain the reflection matrices for the scattering of elementary magnons from certain open boundaries, corresponding to open strings ending on D7 and D5 branes in $AdS_5\times S^5$. In each case we consider two possible orientations for…

High Energy Physics - Theory · Physics 2011-05-24 D. H. Correa , C. A. S. Young

An open supersymmetric t-J chain with boundary fields is studied by means of the Bethe Ansatz. Ground state properties for the case of an almost half-filled band and a bulk magnetic field are determined. Boundary susceptibilities are…

Condensed Matter · Physics 2016-08-31 Fabian H. L. Essler