Classification of 3 + 1 D Bosonic Topological Orders (II): The Case When Some Pointlike Excitations Are Fermions
Name
PhysRevX.9.021005.pdf
Description
Published version
Size
1.19 MB
Format
Adobe PDF
Checksum (MD5)
236f2486adc8cab0df2fb531f725c2ed
Author(s)
Lan, Tian
Wen, Xiao-Gang
Date Issued
2019
Journal
Physical Review X
Publisher
American Physical Society (APS)
Version
Final published version
Abstract
© 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the «https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Topological orders describe a new class of gapped quantum phases of matter at zero temperature, that has various patterns of many-body quantum entanglement. Previously, topological orders in one and two spatial dimensions have been systematically understood and classified. This paper [together with Phys. Rev. X 8, 021074 (2018)PRXHAE2160-330810.1103/PhysRevX.8.021074] develops a systematic and classifying understanding of topological orders in three-dimensional bosonic systems, where the number of topological types for the pointlike and stringlike excitations is assumed to be finite. Our systematic understanding comes from the unique canonical boundary for each 3+1D topological order. We find that the pointlike and stringlike excitations on the canonical boundary are described fully by a mathematical theory - the so-called fusion 2-categories. This theory allows us to classify 3+1D topological orders in bosonic systems in terms of a subset of fusion 2-categories. This systematic understanding further leads to a systematic understanding of 3+1D topological orders in bosonic and fermionic systems with arbitrary finite unitary symmetry.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PHYSREVX.9.021005
