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Fractionalization, topological order, and quasiparticle statistics

Masaki Oshikawa·T. Senthil
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Abstract

We argue, based on general principles, that topological order is essential to realize fractionalization in gapped insulating phases in dimensions $d \geq 2$. In $d=2$ with genus $g$, we derive the existence of the minimum topological degeneracy $q^g$ if the charge is fractionalized in unit of $1/q$, irrespective of microscopic model or of effective theory. Furthermore, if the quasiparticle is either boson or fermion, it must be at least $q^{2g}$.

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Masaki Oshikawa, T. Senthil. 2005-11-29. Fractionalization, topological order, and quasiparticle statistics. https://doi.org/10.1103/physrevlett.96.060601

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