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

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 into interacting fermion systems systematically. 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., no free-fermion and bosonic SPT realizations). Moreover, we also verify the recently conjectured crystalline equivalence principle for 2D interacting fermion systems. Finally, a potential experimental realization of these new classes of point group SPT phases in 2D correlated superconductors is also addressed.