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Published April 11, 2014 | Supplemental Material + Accepted Version + Published
Journal Article Open

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

Abstract

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 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 cannot be realized in any bosonic system. Finally we propose a classification scheme of fermionic SPT phases for any finite, Abelian symmetry.

Additional Information

© 2014 American Physical Society. Received 1 March 2013; Revised manuscript received 29 October 2013; Published 9 April 2014. M. C. thanks Lukasz Fidkowski, Chetan Nayak, Zhenghan Wang, and Juven Wang for insightful discussions. Z.-C. G is supported in part by Frontiers Center with support from the Gordon and Betty Moore Foundation.

Attached Files

Published - PhysRevLett.112.141602.pdf

Accepted Version - 1302.4803v3.pdf

Supplemental Material - suppl.pdf

Supplemental Material - suppl.tex

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