A theory of 2+1D bosonic topological orders
Name
1506.05768.pdf
Description
Accepted version
Size
1.11 MB
Format
Adobe PDF
Checksum (MD5)
744bd143df109a660c52eb13721b77c8
Author(s)
Wen, Xiao-Gang
Date Issued
2016
Journal
National Science Review
Publisher
Oxford University Press (OUP)
Version
Author's final manuscript
Abstract
© The Author(s) 2015. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. All rights reserved. In primary school, we were told that there are four phases of matter: Solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases, ferromagnet, anti-ferromagnet, superfluid, etc. Those phases of matter are so rich, it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. However, there are even more interesting phases of matter that are beyond Landau symmetry breaking theory. In this paper, we review new 'topological' phenomena, such as topological degeneracy, that reveal the existence of those new zero-temperature phase-topologically ordered phases. Microscopically, topologically orders are originated from the patterns of long-range entanglement in the ground states. As a truly new type of order and a truly new kind of phenomena, topological order and long-range entanglement require a new language and a new mathematical framework, such as unitary fusion category and modular tensor category to describe them. In this paper, we will describe a simple mathematical framework based on measurable quantities of topological orders (S, T, c) proposed around 1989. The framework allows us to systematically describe all 2+1D bosonic topological orders (i.e. topological orders in local bosonic/spin/qubit systems).
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/NSR/NWV077
