Classification of two-dimensional fermionic and bosonic topological orders
Name
PhysRevB.91.125149.pdf
Size
4.26 MB
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Adobe PDF
Checksum (MD5)
f8bdad8929fecc3355cc0ec1857e5b94
Author(s)
Gu, Zheng-Cheng
Wang, Zhenghan
Wen, Xiao-Gang
Date Issued
March 2015
Journal
Physical Review B
Publisher
American Physical Society
Citation
Gu, Zheng-Cheng, Zhenghan Wang, and Xiao-Gang Wen. "Classification of two-dimensional fermionic and bosonic topological orders." Phys. Rev. B 91, 125149 (March 2015). © 2015 American Physical Society
Version
Final published version
Abstract
The string-net approach by Levin and Wen, and the local unitary transformation approach by Chen, Gu, and Wen, provide ways to classify topological orders with gappable edge in two-dimensional (2D) bosonic systems. The two approaches reveal that the mathematical framework for (2+1)-dimensional (2+1)D bosonic topological order with gappable edge is closely related to unitary fusion category theory. In this paper, we generalize these systematic descriptions of topological orders to 2D fermion systems. We find a classification of (2+1)D fermionic topological orders with gappable edge in terms of the following set of data (N[ij over k], F[ij over k], F[ijm,αβ over jkn,χδ], d[subscript i]), which satisfy a set of nonlinear algebraic equations. The exactly soluble Hamiltonians can be constructed from the above data on any lattices to realize the corresponding topological orders. When F[ij over k] = 0, our result recovers the previous classification of 2 + 1D bosonic topological orders with gappable edge.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.91.125149
