2-d Fermionic SPT with CRT symmetry

TL;DR

This paper investigates a 2D fermionic symmetry-protected topological phase invariant, showing that imposing CRT symmetry aligns the derived invariant with the conjectured quantum field theory prediction.

Contribution

It demonstrates that the invariant for 2D fermionic SPT phases simplifies to the conjectured form when CRT symmetry is enforced.

Findings

Invariant reduces to the conjectured form under CRT symmetry

CRT symmetry holds automatically in quantum field theory

Provides insight into the role of CRT symmetry in fermionic SPT phases

Abstract

An invariant of SPT-phases with on-site finite group $G$ symmetry for two-dimensional Fermion systems was derived in [O]. This invariant is doubled compared to the conjectured one from the invertible quantum field theory. We show that if we require CRT-symmetry (which holds automatically in quantum field theory) in addition, then our invariant reduces to the conjectured one.