Emergent Supersymmetry at the Boundaries in 1D Charge Conserving Superconductor Coupled to Magnetic Impurities

Interaction induced symmetry protected topological phases exhibit distinct properties which do not exist in the non interacting limit. The topological properties emerge due to strong correlations in the bulk. A well known example is a 1D charge conserving superconductor in the spin triplet phase (STS) with open boundary conditions which features a topological phase with protected Majorana zero modes at the edges. Here we consider a superconductor in the spin singlet phase (SSS) which is considered to be topologically trivial. However upon coupling it to magnetic impurities at the two edges a topological phase will emerge induced by the interplay between the bulk and impurity fluctuations. This phase also exhibits an emergent supersymmetry at the edges in a particular regime of the boundary parameters. We discuss the effect of external fields at the edges that break the supersymmetry and reduces the topological structure to that exhibited by the STS phase