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

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.

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Cited by in corpus (8)

• Integrable approach to simple exclusion processes with boundaries. Review and progress
• The $D(D_3)$-anyon chain: integrable boundary conditions and excitation spectra
• Boundary matrices for the higher spin six vertex model
• Integrable Hamiltonians with $D(D_n)$ symmetry from the Fateev-Zamolodchikov model
• Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry
• Anyon Chains with Pairing Terms
• Reflection equation for the N=3 Cremmer-Gervais R-matrix
• Triangular solutions to the reflection equation for $U_q(\widehat{s{l}_n})$