arXiv Analytics

Sign in

arXiv:0811.1248 [math-ph]AbstractReferencesReviewsResources

Integrable boundary conditions for a non-abelian anyon chain with $D(D_3)$ symmetry

K. A. Dancer, P. E. Finch, P. S. Isaac, J. Links

Published 2008-11-08Version 1

A general formulation of the Boundary Quantum Inverse Scattering Method is given which is applicable in cases where $R$-matrix solutions of the Yang--Baxter equation do not have the property of crossing unitarity. Suitably modified forms of the reflection equations are presented which permit the construction of a family of commuting transfer matrices. As an example, we apply the formalism to determine the most general solutions of the reflection equations for a solution of the Yang-Baxter equation with underlying symmetry given by the Drinfeld double $D(D_3)$ of the dihedral group $D_3$. This $R$-matrix does not have the crossing unitarity property. In this manner we derive integrable boundary conditions for an open chain model of interacting non-abelian anyons.

Related articles: Most relevant | Search more
arXiv:2410.15972 [math-ph] (Published 2024-10-21)
The Yang-Baxter equation, Leibniz algebras, racks and related algebraic structures
arXiv:1307.6808 [math-ph] (Published 2013-07-25, updated 2019-06-17)
Fusion procedure for the Yang-Baxter equation and Schur-Weyl duality
arXiv:math-ph/9911029 (Published 1999-11-23)
[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]