Topological squashed entanglement: Nonlocal order parameter for one-dimensional topological superconductors

Identifying entanglement-based order parameters characterizing topological systems, in particular superconductors and insulators, has remained a major challenge for the physics of quantum matter last two decades. Here we show that end-to-end, long-distance, bipartite squashed entanglement between edges many-body system, defined terms edge-to-edge conditional mutual information, is natural nonlocal parameter one dimension as well quasi one-dimensional geometries. For Kitaev chain entire phase, edge quantized to log(2)/2, half maximal Bell-state entanglement, vanishes trivial phase. Such exhibits correct scaling at phase transition, stable presence interactions, robust against disorder local perturbations. Edge information with respect different multipartitions discriminate from symmetry breaking magnets, shown by comparing fermionic spin-1/2 Ising model transverse field. systems featuring multiple phases numbers modes, like 1D ladder, counts number Majorana excitations distinguishes system. In fact, remain valid detectors superconductivity even tie long-range hopping, geometrical frustration suppressed bulk-edge correspondence.