Many-Body Topological Invariants for Fermionic Symmetry-Protected Topological Phases

Hassan Shapourian, Ken Shiozaki, Shinsei Ryu

Research output: Contribution to journalArticlepeer-review

64 Scopus citations


We define and compute many-body topological invariants of interacting fermionic symmetry-protected topological phases, protected by an orientation-reversing symmetry, such as time-reversal or reflection symmetry. The topological invariants are given by partition functions obtained by a path integral on unoriented spacetime which, as we show, can be computed for a given ground state wave function by considering a nonlocal operation, "partial" reflection or transpose. As an application of our scheme, we study the Z8 and Z16 classification of topological superconductors in one and three dimensions.

Original languageEnglish (US)
Article number216402
JournalPhysical review letters
Issue number21
StatePublished - May 25 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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