An invariant of symmetry protected topological phases with on-site finite group symmetry for two-dimensional Fermion systems

TL;DR

This paper introduces a new invariant for classifying symmetry protected topological phases in two-dimensional fermion systems with finite group symmetries, advancing understanding of their topological properties.

Contribution

It derives a novel invariant that aids in classifying 2D fermionic SPT phases with finite group symmetry, filling a gap in the theoretical framework.

Findings

Derived an invariant for 2D fermionic SPT phases

Provides a classification tool for symmetry protected topological phases

Enhances understanding of fermionic topological invariants

Abstract

We consider SPT-phases with on-site finite group $G$ symmetry for two-dimensional Fermion systems.We derive an invariant of the classification.