Interacting fermionic symmetry-protected topological phases in two dimensions

Understand

We classify and construct models for two-dimensional (2D) interacting fermionic symmetry-protected topological (FSPT) phases with general finite Abelian unitary symmetry $G_f$.

• To obtain the classification, we couple the FSPT system to a dynamical discrete gauge field with gauge group $G_f$ and study braiding statistics in the resulting gauge theory.
• Under reasonable assumptions, the braiding statistics data allows us to infer a potentially complete classification of 2D FSPT phases with Abelian symmetry.
• The FSPT models that we construct are simple stacks of the following two kinds of existing models: (i) free-fermion models and (ii) models obtained through embedding of bosonic symmetry-protected topological (BSPT) phases.