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The construction and classification of symmetry-protected topological (SPT)phases in interacting bosonic and fermionic systems have been intensivelystudied in the past few years. Very recently, a complete classification andconstruction of space group SPT phases were also proposed for interactingbosonic systems. In this paper, we attempt to generalize this classificationand construction scheme systematically into interacting fermion systems. Inparticular, we construct and classify point group SPT phases for 2D interactingfermion systems via lower-dimensional block-state decorations. We discoverseveral intriguing fermionic SPT states that can only be realized ininteracting fermion systems (i.e., not in free-fermion or bosonic SPT systems).Moreover, we also verify the recently conjectured crystalline equivalenceprinciple for 2D interacting fermion systems. Finally, the potentialexperimental realization of these new classes of point group SPT phases in 2Dcorrelated superconductors is addressed.

Construction and classification of point group symmetry protected topological phases in 2D interacting fermionic systems