Topological degeneracy of non-Abelian states for dummies

Abstract

We present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent argument [M.O. and T. Senthil, Phys. Rev. Lett. 96, 060601 (2006)] which relates fraction- alization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61, 10267 (2000)] based on differential geometry is reproduced exactly. Some restrictions on the statistics, due to the fractional charge of the quasiparticle are also discussed. Furthermore, the groundstate degeneracy of the p+ip superconductor in two dimensions, which is closely related to the Pfaffian states, is discussed with a similar construction.

28 pages, 6 figures (version 2: reference on cold atoms added + minor corrections)

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• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
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• Insulator, conductor and commensurability: a topological approach
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