Abstract
Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group D3 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 Z4 parafermion or a minimal model.
Highlights
In recent years there has been a surge of attention directed towards the understanding of many-particle systems exhibiting topological order, i.e. phases which cannot be characterised by a local order parameter
This approach is powerful for anyonic chains, i.e. one-dimensional lattices, where the numerical data can be compared against predictions from conformal field theory (CFT)
In addition we present results for the fusion path chain in support of the expectation that the low energy excitations of the D(D3)-anyon chain are described by the same CFT for all types of boundary conditions studied here, namely products of Z4 parermion and M(5,6) minimal models
Summary
In recent years there has been a surge of attention directed towards the understanding of many-particle systems exhibiting topological order, i.e. phases which cannot be characterised by a local order parameter. Interesting are non-Abelian anyons where the interchange of two particles is described by non-trivial representations of the braid group complemented by fusion rules for the decomposition of product states The fact that these non-Abelian anyons are protected by their topological charge has led to proposals for the use of such systems in universal quantum computation [40, 51]. The phase diagram of the resulting lattice models can be studied based on the numerical computation of finite size spectra This approach is powerful for anyonic chains, i.e. one-dimensional lattices, where the numerical data can be compared against predictions from conformal field theory (CFT). In addition we present results for the fusion path chain in support of the expectation that the low energy excitations of the D(D3)-anyon chain are described by the same CFT for all types of boundary conditions studied here, namely products of Z4 parermion and M(5,6) minimal models
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