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We consider integrable models of the Haldane-Shastry type with open boundary conditions. We define monodromy matrices, obeying the reflection equation, which generate the symmetries of these models. Using a map to the Calogero-Sutherland…

High Energy Physics - Theory · Physics 2023-04-10 D. Bernard. V. Pasquier , D. Serban

We derive the deformed sl(2) Gaudin model with integrable boundaries. Starting from the Jordanian deformation of the SL(2)-invariant Yang R-matrix and generic solutions of the associated reflection equation and the dual reflection equation,…

Exactly Solvable and Integrable Systems · Physics 2014-05-29 N. Cirilo António , N. Manojlović , Z. Nagy

We study solutions of the reflection equation related to the quantum affine algebra $U_q(\widehat{sl_n})$. First, we explain how to construct a family of stochastic integrable vertex models with fixed boundary conditions. Then, we construct…

Mathematical Physics · Physics 2024-06-18 Dmitry Kolyaskin , Vladimir V Mangazeev

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 introduce a spin chain based on finite-dimensional spin-1/2 SU(2) representations but with a non-hermitian `Hamiltonian' and show, using mostly analytical techniques, that it is described at low energies by the SL(2,R)/U(1) Euclidian…

High Energy Physics - Theory · Physics 2015-05-30 Yacine Ikhlef , Jesper Lykke Jacobsen , Hubert Saleur

We diagonalize the double-row transfer matrix of the SU(N) vertex model for certain classes of non-diagonal boundary conditions. We derive explicit expressions for the corresponding eigenvectors and eigenvalues by means of the algebraic…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 W. Galleas , M. J. Martins

The general solutions for the factorization equations of the reflection matrices $K^{\pm}(\theta)$ for the eight vertex and six vertex models (XYZ, XXZ and XXX chains) are found. The associated integrable magnetic Hamiltonians are…

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

The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator…

Mathematical Physics · Physics 2022-12-27 Guang-Liang Li , Junpeng Cao , Panpan Xue , Kun Hao , Pei Sun , Wen-Li Yang , Kangjie Shi , Yupeng Wang

By solving the right reflection equation proposed in reference[16] to describe the Z=0 giant graviton branes, we obtain a boundary matrix with two free parameters for the AdS/CFT SU(1|1) spin chain.

High Energy Physics - Theory · Physics 2009-12-15 Qingyong Lin , Guangliang Li , Yufei Huang

We derive the Bethe Ansatz Equations on the half line for particles interacting through factorized $S$-matrices invariant relative to the centrally extended $su(2|2)$ Lie superalgebra and $su(1|2)$ open boundaries. These equations may be of…

High Energy Physics - Theory · Physics 2009-08-03 W. Galleas

We investigate the thermodynamic limit of the su(n)-invariant spin chain models with unparallel boundary fields. It is found that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy does…

Mathematical Physics · Physics 2017-01-04 Fakai Wen , Tao Yang , Zhanying Yang , Junpeng Cao , Kun Hao , Wen-Li Yang

We introduce a new class of reflected backward stochastic differential equations with two c\`adl\`ag barriers, which need not satisfy any separation conditions. For that reason, in general, the solutions are not semimartingales. We prove…

Probability · Mathematics 2021-03-16 Tomasz Klimsiak

We use boundary quantum group symmetry to obtain recursion formulas which determine nondiagonal solutions of the boundary Yang-Baxter equation (reflection equation) of the XXZ type for any spin j.

High Energy Physics - Theory · Physics 2009-11-07 G. W. Delius , Rafael I. Nepomechie

The double row transfer matrix of the open O(N) spin chain is diagonalized and the Bethe Ansatz equations are also derived by the algebraic Bethe Ansatz method including the so far missing case when the residual symmetry is…

Mathematical Physics · Physics 2018-09-19 Tamas Gombor

We examine super symmetric representations of the B-type Hecke algebra. We exploit such representations to obtain new non-diagonal solutions of the reflection equation associated to the super algebra U_q(gl(m|n)). The boundary super algebra…

Mathematical Physics · Physics 2013-07-09 Anastasia Doikou , Nikos Karaiskos

We study open boundary conditions for the $D^{(2)}_3$ spin chain, which shares connections with the six-vertex model, under staggering, and also to the antiferromagnetic Potts model. By formulating a suitable transfer matrix that is related…

Statistical Mechanics · Physics 2025-09-09 Pete Rigas

We investigate various aspects of the integrability of the vertex models associated to the $D_n^2$ affine Lie algebra with open boundaries. We first study the solutions of the corresponding reflection equation compatible with the minimal…

Exactly Solvable and Integrable Systems · Physics 2009-10-31 M. J. Martins , X. W. Guan

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of…

Statistical Mechanics · Physics 2009-10-30 Anthony J. Bracken , Xiang-Yu Ge , Yao-Zhong Zhang , Huan-Qiang Zhou

We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the $C_{n}^{(1)}$, $D_{n}^{(1)}$ and $A_{2n-1}^{(2)}$ affine Lie algebras. We find three types of solutions with $n$,…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 A. Lima-Santos , R. Malara

We use extensive DMRG calculations to show that a classification of SU(n) spin chains with regard to the existence of spinon confinement and hence a Haldane gap obtained previously for valence bond solid models applies to SU(n) Heisenberg…

Strongly Correlated Electrons · Physics 2015-05-13 S. Rachel , R. Thomale , M. Fuehringer , P. Schmitteckert , M. Greiter