Disentangling interacting symmetry protected phases of fermions in two dimensions*

We explicitly construct the ground states of certain 2+1D fermionic symmetry protected topological (SPT) phases using finite depth circuits of local unitaries. We recover the classification of the so called supercohomology SPT phases and demonstrate that the composition of our unitaries captures the corresponding SPT group structure. Our strategy is to first build an auxiliary bosonic model from group supercohomology data and then employ the recently developed lattice-level fermionization duality to obtain the fermionic SPT. This construction both yields fixed point lattice Hamiltonians that can be defined on arbitrary triangulations and disentangles the roles of supercohomology data and spin structure in fermionic SPT phases. Further, the global symmetry of our circuits implies that these SPT phases can be many-body localized.