Topological response theory of Abelian symmetry-protected topological phases in two dimensions.
It has been shown that the symmetry-protected topological (SPT) phases with finite Abelian symmetries 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 a systematic scheme to classify bosonic SPT phases with any finite Abelian symmetry group. We point out that even for finite Abelian symmetry, there exist bosonic SPT phases beyond the current Chern-Simons theory framework. We also apply the theory to fermionic SPT phases with Zm 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 cannot be realized in any bosonic system. Finally we propose a classification scheme of fermionic SPT phases for any finite, Abelian symmetry.
Station Q, Microsoft Research, Santa Barbara, California 93106, USA and Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Meng
M
Cheng
Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA and Department of Physics, California Institute of Technology, Pasadena, California 91125, USA.
Zheng-Cheng
ZC
Gu