1204.0520 (Evelyn Tang et al.)

Interaction effects on 1D fermionic symmetry protected topological
phases    [PDF]

Evelyn Tang, Xiao-Gang Wen

In free fermion systems with given symmetry and dimension, the possible topological phases are labeled by elements of only three types of Abelian groups, Z_1, Z_2, or Z. For example non-interacting 1D fermionic superconducting phases with S_z spin rotation and time reversal symmetries are classified by Z. With interactions the results are more varied. Here we show that weakly interacting 1D fermionic superconducting phases with S_z spin rotation and time reversal symmetries are classified by Z_4. Using group cohomology, one can show that there are four and only four distinct phases for such 1D superconductors even with strong interactions. Thus all four symmetry protected topological phases of 1D fermionic superconductors with S_z spin rotation and time reversal symmetries can be realized by free fermions. We also show that 1D fermionic superconducting phases with Z_n discrete S_z spin rotation and time reversal symmetries are classified by Z_4 when n=even and Z_2 when n=odd. Again, all these strongly interacting symmetry protected topological phases can be realized by non-interacting fermions.

View original: http://arxiv.org/abs/1204.0520