Fermionic Symmetry Protected Topological Phases and Cobordisms

Creators: Kapustin, Anton; Thorngren, Ryan; Turzillo, Alex; Wang, Zitao

Abstract

It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with Z_2 symmetry, where Z_2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimension D ≤ 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases.

Additional Information

© 2015 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: August 18, 2015; Accepted: November 25, 2015; Published: December 10, 2015. R.T. would like to thank Xie Chen for patiently answering his questions and Rob Kirby for an enlightening discussion. A. K. would like to acknowledge conversations with Alexei Kitaev and Zhengcheng Gu. The work of A.K., A.T., and Z.W. was supported in part DOE grant DE-FG02-92ER40701.

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Published - 10.1007_2FJHEP12_2015_052.pdf

Submitted - 1406.7329v1.pdf

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