Supersymmetric boundaries of one-dimensional phases of fermions beyond SPTs

It has recently been demonstrated that protected supersymmetry emerges on the boundaries of one-dimensional intrinsically fermionic symmetry protected trivial (SPT) phases. Here we investigate the case of one-dimensional fermionic short-range entangled (SRE) phases beyond SPT phases. We show that for SRE phases that are not SPT phases, boundary supersymmetry is neither protected nor forbidden by the bulk SRE phase, and hence amounts to a choice of boundary condition. We characterize this choice as a group cohomology class and study the behavior of supersymmetric boundary conditions under the stacking of the bulk SRE phases.