1302.4803 (Meng Cheng et al.)

Topological Response Theory of Abelian Symmetry-Protected Topological
Phases in Two Dimensions    [PDF]

Meng Cheng, Zheng-Cheng Gu

We systematically characterize the symmetry-protected topological (SPT) phases with finite Abelian symmetries that can be described by Chern-Simons field theory. We propose a topological response theory to uniquely identify the SPT orders, which allows us to obtain an (almost)complete characterization of bosonic SPT phases with any finite Abelian symmetry group. We then compare our results with the recently proposed group cohomolgy approach and discuss the limitation of the Chern-Simons theory approach. We show that even for finite Abelian symmetry, there exist bosonic SPT phases beyond the Chern-Simons theory framework. We also apply the theory to fermionic SPT with Z_m symmetry and find the classification of SPT phases depends on the parity of m: for even m there are 2m classes, m out of which is intrinsically fermionic SPT phases and can not be realized in any bosonic system. Finally we propose a classification scheme of fermionic SPT phases for any finite, Abelian symmetry.

View original: http://arxiv.org/abs/1302.4803