Non-abelian statistics from an abelian model

Abstract

It is well known that the abelian $Z_2$ anyonic model (toric code) can be realized on a highly entangled two-dimensional spin lattice, where the anyons are quasiparticles located at the endpoints of string-like concatenations of Pauli operators. Here we show that the same entangled states of the same lattice are capable of supporting the non-abelian Ising model, where the concatenated operators are elements of the Clifford group. The Ising anyons are shown to be essentially superpositions of the abelian toric code anyons, reproducing the required fusion, braiding and statistical properties. We propose a string framing and ancillary qubits to implement the non-trivial chirality of this model.

5 pages, 3 figures

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• Topological spin liquids in the ruby lattice with anisotropic Kitaev interactions
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• Non-Abelian statistics with mixed-boundary punctures on the toric code
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• Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids
• Local realizations of anyon exchange symmetries without lattice dislocations
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• Topological phase diagram of $\mathcal{D}(S_3)$ induced by forbidding charges and fluxes