Symmetry-protected topological phases in noninteracting fermion systems
Name
Wen-2012-Symmetry-protected topological phases.pdf
Size
251.74 KB
Format
Adobe PDF
Checksum (MD5)
358a6156d2bf2ed24e168b013072d4ce
Author(s)
Wen, Xiao-Gang
Date Issued
February 2012
Journal
Physical Review B
Publisher
American Physical Society
Citation
Wen, Xiao-Gang. “Symmetry-protected Topological Phases in Noninteracting Fermion Systems.” Physical Review B 85.8 (2012). ©2012 American Physical Society
Version
Final published version
Abstract
Symmetry-protected topological (SPT) phases are gapped quantum phases with a certain symmetry, which can all be smoothly connected to the same trivial product state if we break the symmetry. For noninteracting fermion systems with time reversal (T̂), charge conjugation (Ĉ), and/or U(1) (N̂) symmetries, the total symmetry group can depend on the relations between those symmetry operations, such as T̂N̂T̂[superscript −1]=N̂ or T̂N̂T̂−1=−N̂. As a result, the SPT phases of those fermion systems with different symmetry groups have different classifications. In this paper, we use Kitaev's K-theory approach to classify the gapped free-fermion phases for those possible symmetry groups. In particular, we can view the U(1) as a spin rotation. We find that superconductors with the S[subscript z] spin-rotation symmetry are classified by Z in even dimensions, while superconductors with the time reversal plus the Sz spin-rotation symmetries are classified by Z in odd dimensions. We show that all 10 classes of gapped free-fermion phases can be realized by electron systems with certain symmetries. We also point out that, to properly describe the symmetry of a fermionic system, we need to specify its full symmetry group that includes the fermion number parity transformation (−)[superscript N̂]. The full symmetry group is actually a projective symmetry group.
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.85.085103
