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

TL;DR

This paper develops a generalized boundary quantum inverse scattering method applicable to non-crossing unitarity R-matrices, and applies it to derive integrable boundary conditions for a non-abelian anyon chain with D(D_3) symmetry.

Contribution

It introduces a modified formalism for the boundary quantum inverse scattering method applicable to non-crossing R-matrices and applies it to a non-abelian anyon model with D(D_3) symmetry.

Findings

Derived the most general solutions to reflection equations for D(D_3) symmetric R-matrix.

Constructed integrable boundary conditions for a non-abelian anyon chain.

Extended the boundary quantum inverse scattering method to non-crossing unitarity cases.

Abstract

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.