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We generalize the hierarchy construction to generic 2+1D topological orders (which can be non-Abelian) by condensing Abelian anyons in one topological order to construct a new one.
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This is different from the so called “anyon condensation” categorical approach where only bosons condensing into the trivial state is considered
Cited in the paper.
Physically this amounts to condensing the fermionic quasiparticle into an integer quantum Hall state. If we instead condense the fermionic quasiparticle into p ± i p p\pm\mathrm{i}p states we are able to obtain the “sixteen fold way”. However, such condensation is beyond the construction of this work
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2016
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M. Barkeshli, P. Bonderson, C.-M. Jian, M. Cheng, and K. Walker, (2016), arXiv:1612.07792
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T. Lan, L. Kong, and X.-G. Wen, Commun. Math. Phys. 351
2017
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