English

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

Mathematical Physics 2013-01-03 v1 Mesoscale and Nanoscale Physics math.MP Exactly Solvable and Integrable Systems

Abstract

A general formulation of the Boundary Quantum Inverse Scattering Method is given which is applicable in cases where RR-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(D3)D(D_3) of the dihedral group D3D_3. This RR-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.

Keywords

Cite

@article{arxiv.0811.1248,
  title  = {Integrable boundary conditions for a non-abelian anyon chain with $D(D_3)$ symmetry},
  author = {K. A. Dancer and P. E. Finch and P. S. Isaac and J. Links},
  journal= {arXiv preprint arXiv:0811.1248},
  year   = {2013}
}