The $D(D_{3})$-anyon chain: integrable boundary conditions and excitation spectra

TL;DR

This paper constructs and analyzes integrable chains of non-Abelian anyons with D3 symmetry, exploring their boundary conditions, spectra, and associated conformal field theories, revealing rich low-energy behaviors.

Contribution

It introduces a new integrable anyonic model based on D3 symmetry, connecting it to known face models and analyzing its spectra and conformal limits.

Findings

The model exhibits integrability with various boundary conditions.

Finite size spectra match predictions from conformal field theory.

The continuum limit involves either Z4 parafermion or minimal models.

Abstract

Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group $D_3$ are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a $Z_4$ parafermion or a $\mathcal{M}_{(5,6)}$ minimal model.