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.