Splitting the Topological Degeneracy of non-Abelian Anyons

Details Splitting the Topological Degeneracy of non-Abelian Anyons Splitting the Topological Degeneracy of non-Abelian Anyons

2009-05-17

arxiv.org/abs/0905.2726v2

Phys. Rev. Lett. 103, 110403 (2009)

Physics

Quantum Physics

5 pages; v2 clarifying changes and corrections

Scientific paper

10.1103/PhysRevLett.103.110403

We examine tunneling of topological charge between non-Abelian anyons as a perturbation of the long-range effective theory of a topologically ordered system. We obtain energy corrections in terms of the anyons' universal algebraic structure and non-universal tunneling amplitudes. We find that generic tunneling completely lifts the topological degeneracy of non-Abelian anyons. This degeneracy splitting is exponentially suppressed for long distances between anyons, but leaves no topological protection at shorter distances. We also show that general interactions of anyons can be expressed in terms of the transfer of topological charge, and thus can be treated effectively as tunneling interactions.

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