Symmetry protected topological phases in non-interacting fermion systems

Details Symmetry protected topological phases in non-interacting fermion systems Symmetry protected topological phases in non-interacting fermion systems

2011-11-28

arxiv.org/abs/1111.6341v1

Phys. Rev. B 85, 085103 (2012)

Physics

Condensed Matter

Strongly Correlated Electrons

15 pages, RevTeX4, 7 tables

Scientific paper

10.1103/PhysRevB.85.085103

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 non-interacting fermion systems with time reversal (T), charge conjugation (C), and/or U(1) (N) symmetries, the total symmetry group can depend on the relations between those symmetry operations, such as T N T^{-1}= N or T N T^{-1}= -N. 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_z spin rotation symmetry are classified by Z in even dimensions, while superconductors with the time reversal plus the S_z 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 (-)^N. The full symmetry group is actually a projective symmetry group.

Affiliated with

Also associated with

No associations

Rating

Symmetry protected topological phases in non-interacting fermion systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Symmetry protected topological phases in non-interacting fermion systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symmetry protected topological phases in non-interacting fermion systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-66870