Fractionalization, topological order, and quasiparticle statistics

TL;DR

This paper establishes that topological order is crucial for fractionalization in gapped insulators in two or more dimensions, deriving minimum degeneracies related to the fractional charge and quasiparticle statistics.

Contribution

It provides a general theoretical framework linking topological order to fractionalization and quasiparticle statistics in higher-dimensional insulators.

Findings

Minimum topological degeneracy is q^g for fractionalized charge in genus g surfaces.

Quasiparticles that are bosons or fermions have degeneracy at least q^{2g}.

Topological order is necessary for fractionalization in gapped phases in dimensions ≥ 2.

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 $q^{2g}$.