Topological classification of one-dimensional chiral symmetric interfaces

We address the topological classification of one-dimensional chiral symmetric interfaces embedded into a two-dimensional substrate. A proof of the validity of a topological classification based on the Green's function by explicit evaluation of the topological invariant is presented. Further, we show that due to entanglement between the in-gap modes and the substrate, the full physics of the substrate that is contained in the Green's function is required. This is done by considering a classification scheme derived from the reduced ground state projector, for which we show that an uncritical handling produces erroneous changes in the topological index due to entanglement driven gap closures. We illustrate our results by applying them to a tight-binding model of a spiral magnetic interface in a 𝑠-wave superconductor.