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We present the general diagonal and, in some cases, non-diagonal solutions of the boundary Yang-Baxter equation for a number of related interaction-round-a-face models, including the standard and dilute A_L, D_L and E_{6,7,8} models.

Statistical Mechanics · Physics 2009-10-28 Roger E. Behrend , Paul A. Pearce

We further study integrable deformations of the AdS$_5\times$S$^5$ superstring by following the Yang-Baxter sigma model approach with classical $r$-matrices satisfying the classical Yang-Baxter equation (CYBE). Deformed string backgrounds…

High Energy Physics - Theory · Physics 2014-12-12 Takuya Matsumoto , Kentaroh Yoshida

We consider a general class of boundary terms of the open XYZ spin-1/2 chain compatible with integrability. We have obtained the general elliptic solution of $K$-matrix obeying the boundary Yang-Baxter equation using the $R$-matrix of the…

High Energy Physics - Theory · Physics 2009-10-28 Takeo Inami , Hitoshi Konno

We explore the algebraic structure of a particular ansatz of Yang Baxter Equation which is inspired from the Bethe Ansatz treatment of the ASEP spin-model. Various classes of Hamiltonian density arriving from two types of R-Matrices are…

Statistical Mechanics · Physics 2024-11-19 Suvendu Barik , Alexander. S. Garkun , Vladimir Gritsev

We explicitly construct and classify all Jordanian solutions of the classical Yang-Baxter equation on $\mathfrak{psu}(2,2|4)$, corresponding to Jordanian Yang-Baxter deformations of the $AdS_5\times S^5$ superstring. Such deformations…

High Energy Physics - Theory · Physics 2023-06-14 Riccardo Borsato , Sibylle Driezen

We study integrable deformations of two-dimensional non-linear sigma-models and present a new class of classical solutions to critical bi-Yang-Baxter models for general groups. For the simplest example, namely the SL(2,R) bi-Yang-Baxter…

High Energy Physics - Theory · Physics 2022-12-09 Thomas W. Grimm , Jeroen Monnee

Involutive non-degenerate set theoretic solutions of the Yang-Baxter equation are considered, with a focus on finite solutions. A rich class of indecomposable and irretractable solutions is determined and necessary and sufficient conditions…

Quantum Algebra · Mathematics 2021-12-15 Ferran Cedó , Jan Okniński

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 introduce and solvev a special family of integrable interacting vertex models that generalizes the well known six-vertex model. In addition to the usual nearest-neighbor interactions among the vertices, there exist extra hard-core…

Statistical Mechanics · Physics 2009-11-13 Francisco C. Alcaraz , Matheus J. Lazo

We derive and classify all regular solutions of the boundary Yang-Baxter equation for 19-vertex models known as Zamolodchikov-Fateev or $A_{1}^{(1)}$ model, Izergin-Korepin or $A_{2}^{(2)}$ model, sl(2|1) model and osp(2|1) model. We find…

solv-int · Physics 2009-10-31 A. Lima-Santos

In this paper we discuss and characterize several set-theoretic solutions of the Yang-Baxter equation obtained using skew lattices, an algebraic structure that has not yet been related to the Yang-Baxter equation. Such solutions are…

Quantum Algebra · Mathematics 2020-02-06 Karin Cvetko-Vah , Charlotte Verwimp

We work towards the classification of all one-dimensional exclusion processes with two species of particles that can be solved by a nested coordinate Bethe Ansatz. Using the Yang-Baxter equations, we obtain conditions on the model…

Statistical Mechanics · Physics 2023-07-12 Ivan Lobaskin , Martin R Evans , Kirone Mallick

Expanding upon earlier results [arXiv:1702.02861], we present a compendium of $\sigma$-models associated with integrable deformations of AdS$_5$ generated by solutions to homogenous classical Yang-Baxter equation. Each example we study from…

High Energy Physics - Theory · Physics 2018-05-23 Thiago Araujo , Ilya Bakhmatov , Eoin Ó Colgáin , Jun-ichi Sakamoto , Mohammad M. Sheikh-Jabbari , Kentaroh Yoshida

Two-dimensional $\sigma$-models with $\mathbb{Z}_N$-symmetric homogeneous target spaces have been shown to be classically integrable when introducing WZ-terms in a particular way. This article continues the search for new models of this…

High Energy Physics - Theory · Physics 2022-07-13 David Osten

We present most general one-parametric solutions of the Yang-Baxter equations (YBE) for one spectral parameter dependent $R_{ij}(u)$-matrices of the six- and eight-vertex models, where the only constraint is the particle number conservation…

Mathematical Physics · Physics 2013-05-09 Sh. Khachatryan , A. Sedrakyan

The formal derivatives of the Yang-Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations. The derivatives of the $R$ matrix…

Exactly Solvable and Integrable Systems · Physics 2021-07-07 R. S. Vieira , A. Lima-Santos

We consider \gamma-deformations of the AdS_5xS^5 superstring as Yang-Baxter sigma models with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). An essential point is that the classical r-matrices are composed of…

High Energy Physics - Theory · Physics 2015-06-19 Takuya Matsumoto , Kentaroh Yoshida

In this paper, the relations between the Yang-Baxter equation and affine actions are explored in detail. In particular, we classify solutions of the Yang-Baxter equations in two ways: (i) by their associated affine actions of their…

Quantum Algebra · Mathematics 2016-07-13 Dilian Yang

We present an integrable deformation of the $AdS_{5}\times S^{5}$ pure spinor action based on homological perturbation theory. Its equations of motion, Lax connection and BRST symmetry are discussed. The resulting model describes a pure…

High Energy Physics - Theory · Physics 2019-02-20 Hector A. Benitez , Victor O. Rivelles

We introduce non-degenerate solutions of the Yang-Baxter equation in the setting of symmetric monoidal categories. Our theory includes non-degenerate set-theoretical solutions as basic examples. However, infinite families of non-degenerate…

Quantum Algebra · Mathematics 2018-04-04 J. A. Guccione , J. J. Guccione , L. Vendramin