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A special case of the Fateev-Zamolodchikov model is studied resulting in a solution of the Yang-Baxter equation with two spectral parameters. Integrable models from this solution are shown to have the symmetry of the Drinfeld double of a…

Mathematical Physics · Physics 2012-11-20 P. E. Finch

Let $R$ be a Hecke solution to the Yang-Baxter equation and $K$ be a reflection equation matrix with coefficients in an associative algebra $\A$. Let $R(x)$ be the baxterization of $R$ and suppose that $K$ satisfies a polynomial equation…

Quantum Algebra · Mathematics 2009-11-11 P. P. Kulish , A. I. Mudrov

We derive the solutions of the boundary Yang-Baxter equation associated with a supersymmetric nineteen vertex model constructed from the three-dimensional representation of the twisted quantum affine Lie superalgebra…

Exactly Solvable and Integrable Systems · Physics 2017-09-13 R. S. Vieira , A. Lima Santos

We show that the one dimensional, critical transverse field Ising model is Yang-Baxter integrable. This is done by constructing commuting transfer matrices built out of a $R$-matrix satisfying the Yang-Baxter equation with additive spectral…

High Energy Physics - Theory · Physics 2025-10-13 Akash Sinha , Tinu Justin , Pramod Padmanabhan , Vladimir Korepin

The Yang-Baxter Equation (YBE) plays a crucial role for studying integrable many-body quantum systems. Many known YBE solutions provide various examples ranging from quantum spin chains to superconducting systems. Models of solvable…

Quantum Physics · Physics 2024-11-19 Alexander. S. Garkun , Suvendu K. Barik , Aleksey K. Fedorov , Vladimir Gritsev

We construct new non-diagonal solutions to the boundary Yang-Baxter-Equation corresponding to a two-dimensional field theory with U_q(a_2^(1)) quantum affine symmetry on a half-line. The requirements of boundary unitarity and boundary…

High Energy Physics - Theory · Physics 2014-11-18 Georg M. Gandenberger

The Yang-Baxter equation has long been recognised as the masterkey to integrability, providing the basis for exactly solved models which capture the fundamental physics of a number of realistic classical and quantum systems. In this article…

Statistical Mechanics · Physics 2016-04-22 Murray T. Batchelor , Angela Foerster

We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang-Baxter equations, coactions, fusions, and commuting traces are derived. Explicit…

Mathematical Physics · Physics 2020-09-25 J. Avan , E. Ragoucy

A review of some recent results on the dynamical theory of the Yang-Baxter maps (also known as set-theoretical solutions to the quantum Yang-Baxter equation) is given. The central question is the integrability of the transfer dynamics. The…

Quantum Algebra · Mathematics 2007-05-23 A. P. Veselov

Starting from the Kauffman-Lomonaco braiding matrix transforming the natural basis to Bell states, the spectral parameter describing the entanglement is introduced through Yang-Baxterization. It gives rise to a new type of solutions for…

Quantum Physics · Physics 2019-05-22 Li-Wei Yu , Mo-Lin Ge

We investigate the possible regular solutions of the boundary Yang-Baxter equation for the fundamental $U_q[G_2]$ vertex model. We find four distinct classes of reflection matrices such that half of them are diagonal while the other half…

Exactly Solvable and Integrable Systems · Physics 2010-04-08 A. Lima-Santos , M. J. Martins

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum…

Mathematical Physics · Physics 2021-07-23 Vladimir V. Bazhanov , Sergey M. Sergeev

We construct sets of structure matrices for the semi-dynamical reflection algebra, solving the Yang-Baxter type consistency equations extended by the action of an automorphism of the auxiliary space. These solutions are parametrized by…

Quantum Algebra · Mathematics 2015-06-26 Jean Avan , Geneviève Rollet

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite interval at zero density. $R$-matrix and monodromy matrix are obtained as limits from their known counterparts on the finite interval.…

Condensed Matter · Physics 2009-10-28 Shuichi Murakami , Frank Göhmann

The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2 grading along both chain and time directions is presented. The XXZ model with staggered disposition along a chain of both, the anisotropy \pm\Delta, as well as…

High Energy Physics - Theory · Physics 2007-05-23 D. Arnaudon , R. Poghossian , A. Sedrakyan , P. Sorba

Yang-Baxter integrable vertex models with a generic $\mathbb{Z}_2$-staggering can be expressed in terms of composite $\mathbb{R}$-matrices given in terms of the elementary $R$-matrices. Similarly, integrable open boundary conditions can be…

Statistical Mechanics · Physics 2023-01-30 Holger Frahm , Sascha Gehrmann

An explicit quantization is given of certain skew-symmetric solutions of the classical Yang-Baxter, yielding a family of $R$-matrices which generalize to higher dimensions the Jordanian $R$-matrices. Three different approaches to their…

Quantum Algebra · Mathematics 2007-05-23 Robin Endelman , Timothy J. Hodges

We obtain two series of spectral parameter dependent solutions to the generalized Yang-Baxter equations (GYBE), for definite types of $N_1^2\times N_2^2$ matrices with general dimensions $N_1$ and $N_2$. Appropriate extensions are presented…

Mathematical Physics · Physics 2023-10-27 Shahane A. Khachatryan

Interaction-Round the Face (IRF) models are two-dimensional lattice models of statistical mechanics defined by an affine Lie algebra and admissibility conditions depending on a choice of representation of that affine Lie algebra. Integrable…

High Energy Physics - Theory · Physics 2023-08-22 Vladimir Belavin , Doron Gepner , J. Ramos Cabezas , Boris Runov

We study scattering of three equal mass particles in one dimension. Integrable interactions are synonymous with non-diffractive scattering, meaning that the set of incoming momenta for any scattering event coincides with the set of outgoing…

Quantum Gases · Physics 2013-05-30 Austen Lamacraft