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We introduce a class of particle models in one dimension involving exchange interactions that have scattering properties satisfying the Yang-Baxter consistency condition. A subclass of these models exhibits reflectionless scattering, in…

High Energy Physics - Theory · Physics 2022-02-10 Alexios P. Polychronakos

We consider the critical non-unitary minimal model {\cal M}(3,5) with integrable boundaries. We analyze the patterns of zeros of the eigenvalues of the transfer matrix and then determine the spectrum of the critical theory through the…

High Energy Physics - Theory · Physics 2018-03-13 Omar El Deeb

The exotic bialgebra S03, defined by a solution of the Yang-Baxter equation, which is not a deformation of the trivial, is considered. Its FRT dual algebra $s03_F$ is studied. The Baxterisation of the dual algebra is given in two different…

Quantum Algebra · Mathematics 2009-11-11 D. Arnaudon , A. Chakrabarti , V. K. Dobrev , S. G. Mihov

We start from known solutions of the Yang-Baxter equation with a spectral parameter defined on the tensor product of two infinite-dimensional principal series representations of the group $\mathrm{SL}(2,\mathbb{C})$ or Faddeev's modular…

Mathematical Physics · Physics 2016-03-14 Dmitry Chicherin , Sergey E. Derkachov , Vyacheslav P. Spiridonov

We investigate integrable boundary conditions (BCs) for the principal chiral model on the half-line, and rational solutions of the boundary Yang-Baxter equation (BYBE). In each case we find a connection with (type I, Riemannian, globally)…

High Energy Physics - Theory · Physics 2014-11-18 N. J. MacKay , B. J. Short

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 consider two a priori very different problems: construction of the eigenstates of the spin chains with non parallel boundary magnetic fields and computation of the partition function for the trigonometric solid-on-solid…

Mathematical Physics · Physics 2015-03-17 Ghali Filali , Nikolai Kitanine

Generalization of the quantum Yang-Baxter equation solutions to an arbitrary grading is studied. The noncommutative differential calculi corresponding to such solutions is considered. The connection with the ordinary and supersymmetric…

Quantum Algebra · Mathematics 2007-05-23 W. Marcinek

Yangian symmetry of amplitudes in $\mathcal{N}=4$ super Yang-Mills theory is formulated in terms of eigenvalue relations for monodromy matrix operators. The Quantum Inverse Scattering Method provides the appropriate tools to treat the…

High Energy Physics - Theory · Physics 2015-06-17 D. Chicherin , S. Derkachov , R. Kirschner

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 present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary…

Mathematical Physics · Physics 2016-08-09 Sabina Alazzawi , Gandalf Lechner

We present resent results regarding invertible, non-degenerate solutions of the set-theoretic Yang-Baxter and reflection equations. We recall the notion of braces and we present and prove various fundamental properties required for the…

Quantum Algebra · Mathematics 2025-05-21 Anastasia Doikou

As is well known, the type 1 Lie superalgebra sl(r+1|s+1) admits a one parameter family of finite dimensional irreducible representations. We have carried out an analytic Bethe ansatz related to this family of representations. We present…

Mathematical Physics · Physics 2009-12-15 Zengo Tsuboi

We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We formulate the analytical Bethe Ansatz…

Quantum Algebra · Mathematics 2010-04-05 D. Arnaudon , J. Avan , N. Crampe' , A. Doikou , L. Frappat , E. Ragoucy

We prove, using the coordinate Bethe ansatz, the exact solvability of a model of three particles whose point-like interactions are determined by the root system of g_2. The statistics of the wavefunction are left unspecified. Using the…

Mathematical Physics · Physics 2007-05-23 N. Crampe , C. A. S. Young

We propose a trigonometric solution of the associative Yang-Baxter equation related to the queer Lie superalgebra which in its turn satisfies the quantum Yang-Baxter equation.

Mathematical Physics · Physics 2024-12-30 Maria Matushko

We propose that the Baxter's $Q$-operator for the XYZ quantum spin chain with open boundary conditions is given by the $j\to \infty$ limit of the corresponding transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. The…

High Energy Physics - Theory · Physics 2010-04-05 Wen-Li Yang , Yao-Zhong Zhang

A coloured braid group representation (CBGR) is constructed with the help of some modified universal ${\cal R}$-matrix, associated to $U_q(gl(2))$ quantised algebra. Explicit realisation of Faddeev-Reshetikhin-Takhtajan (FRT) algebra is…

High Energy Physics - Theory · Physics 2008-02-03 B. Basu-Mallick

From the q-oscillator solution to the tetrahedron equation associated with a quantized coordinate ring, we construct solutions to the Yang-Baxter equation by applying a reduction procedure formulated earlier by S. Sergeev and the first…

Mathematical Physics · Physics 2013-11-14 Atsuo Kuniba , Masato Okado

We formulate the algebraic Bethe ansatz solution of the SU(N) vertex models with rather general non-diagonal toroidal boundary conditions. The reference states needed in the Bethe ansatz construction are found by performing gauge…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 G. A. P. Ribeiro , M. J. Martins , W. Galleas