Many-body topological invariants for fermionic symmetry-protected topological phases

Hassan Shapourian; Ken Shiozaki; Shinsei Ryu

doi:10.1103/physrevlett.118.216402

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arXiv · 1607.03896

Many-body topological invariants for fermionic symmetry-protected topological phases

Hassan Shapourian·Ken Shiozaki·Shinsei Ryu

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Abstract

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 non-local operation, "partial" reflection or transpose. As an application of our scheme, we study the $\mathbb{Z}_8$ and $\mathbb{Z}_{16}$ classification of topological superconductors in one and three dimensions.

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Hassan Shapourian, Ken Shiozaki, Shinsei Ryu. 2017-05-29. Many-body topological invariants for fermionic symmetry-protected topological phases. https://doi.org/10.1103/physrevlett.118.216402

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