Many-Body Chern Number from Statistical Correlations of Randomized Measurements

One of the main topological invariants that characterizes several topologically-ordered phases is many-body Chern number (MBCN). Paradigmatic examples include fractional quantum Hall phases, which are expected to be realized in different atomic and photonic platforms near future. Experimental measurement numerical computation this invariant conventionally based on linear-response techniques require having access a family states, as function an external parameter, not suitable for many simulators. Here, we propose ancilla-free experimental scheme invariant, without requiring any knowledge Hamiltonian. Specifically, use statistical correlations randomized measurements infer MBCN wavefunction. Remarkably, our results apply disk-like geometries more amenable current simulator architectures.