Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations
Name
PhysRevB.91.075114.pdf
Size
1.24 MB
Format
Adobe PDF
Checksum (MD5)
f52c29986855019136b57b4e5af071bf
Author(s)
Moradi, Heidar
Wen, Xiao-Gang
Date Issued
February 2015
Journal
Physical Review B
Publisher
American Physical Society
Citation
Moradi, Heidar, and Xiao-Gang Wen. “Universal Topological Data for Gapped Quantum Liquids in Three Dimensions and Fusion Algebra for Non-Abelian String Excitations.” Physical Review B 91.7 (2015). © 2015 American Physical Society
Version
Final published version
Abstract
Recently we conjectured that a certain set of universal topological quantities characterize topological order in any dimension. Those quantities can be extracted from the universal overlap of the ground-state wave functions. For systems with gapped boundaries, these quantities are representations of the mapping class group MCG(M) of the space manifold M on which the systems live. We will here consider simple examples in three dimensions and give physical interpretation of these quantities, related to the fusion algebra and statistics of particles and string excitations. In particular, we will consider dimensional reduction from 3+1D to 2+1D, and show how the induced 2+1D topological data contain information on the fusion and the braiding of non-Abelian string excitations in 3D. These universal quantities generalize the well-known modular S and T matrices to any dimension.
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/PhysRevB.91.075114
