Bulk topological signatures of a quasicrystal

We show how measuring real space properties such as the charge density in a quasiperiodic system can be used to gain insight into their topological properties. In particular, for Fibonacci chain, we that total onsite oscillates when plotted appropriate coordinates, and number of oscillations is given by Chern gap which Fermi level lies. these have two distinct interpretations, obtained extrapolating results from extreme limits chain -- valence bond picture strong modulation limit, perturbation around periodic weak limit. This effect found remain robust at moderate interactions, well presence disorder. conclude experimental measurement distribution yield information on straightforward way.