Hierarchy Construction and Non-Abelian Families of Generic Topological Orders
Name
PhysRevLett.119.040403.pdf
Size
124.21 KB
Format
Adobe PDF
Checksum (MD5)
7281374c29c52cd6c8a2b3416b2e7094
Author(s)
Lan, Tian
Wen, Xiao-Gang
Date Issued
July 2017
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Lan, Tian and Wen, Xiao-Gang. "Hierarchy Construction and Non-Abelian Families of Generic Topological Orders." Physical Review Letters 119, 4: 040403 © 2017 American Physical Society
Version
Final published version
Abstract
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. We show that such construction is reversible and leads to a new equivalence relation between topological orders. We refer to the corresponding equivalence class (the orbit of the hierarchy construction) as “the non-Abelian family.” Each non-Abelian family has one or a few root topological orders with the smallest number of anyon types. All the Abelian topological orders belong to the trivial non-Abelian family whose root is the trivial topological order. We show that Abelian anyons in root topological orders must be bosons or fermions with trivial mutual statistics between them. The classification of topological orders is then greatly simplified, by focusing on the roots of each family: those roots are given by non-Abelian modular extensions of representation categories of Abelian groups.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PhysRevLett.119.040403
