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Topological degeneracy of non-Abelian states for dummies

Masaki Oshikawa·Yong Baek Kim·Kirill Shtengel·Chetan Nayak·Sumanta Tewari
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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.

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Masaki Oshikawa, Yong Baek Kim, Kirill Shtengel, Chetan Nayak, Sumanta Tewari. 2006-09-27. Topological degeneracy of non-Abelian states for dummies. https://doi.org/10.1016/j.aop.2006.08.001

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