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

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

2008-11-08

arxiv.org/abs/0811.1248v1

Physics

Mathematical Physics

Scientific paper

10.1016/j.nuclphysb.2008.12.002

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.

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