  The construction and classification of symmetry-protected topological (SPT)
phases in interacting bosonic and fermionic systems have been intensively
studied in the past few years. Very recently, a complete classification and
construction of space group SPT phases were also proposed for interacting
bosonic systems. In this paper, we attempt to generalize this classification
and construction scheme systematically into interacting fermion systems. In
particular, we construct and classify point group SPT phases for 2D interacting
fermion systems via lower-dimensional block-state decorations. We discover
several intriguing fermionic SPT states that can only be realized in
interacting fermion systems (i.e., not in free-fermion or bosonic SPT systems).
Moreover, we also verify the recently conjectured crystalline equivalence
principle for 2D interacting fermion systems. Finally, the potential
experimental realization of these new classes of point group SPT phases in 2D
correlated superconductors is addressed.
