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We construct fixed point lattice models for group supercohomology symmetryprotected topological (SPT) phases of fermions in 2+1D. A key feature of ourapproach is to construct finite depth circuits of local unitaries thatexplicitly build the ground states from a tensor product state. We then recoverthe classification of fermionic SPT phases, including the group structure understacking, from the algebraic composition rules of these circuits. Furthermore,we show that the circuits are symmetric, implying that the groupsupercohomology phases can be many body localized. Our strategy involves firstbuilding an auxiliary bosonic model, and then fermionizing it using the dualityof Chen, Kapustin, and Radicevic. One benefit of this approach is that itclearly disentangles the role of the algebraic group supercohomology data,which is used to build the auxiliary bosonic model, from that of the spinstructure, which is combinatorially encoded in the lattice and enters only inthe fermionization step. In particular this allows us to study our models on 2dspatial manifolds of any topology and to define a lattice-level procedure forungauging fermion parity.

Disentangling interacting symmetry protected phases of fermions in two dimensions