Measurement of topological order based on metric-curvature correspondence

A unified expression for topological invariants has been proposed recently to describe the order in Dirac models belonging any dimension and symmetry class. We uncover a correspondence between curvature function that integrates this invariant quantum metric measures distance properly defined many-body Bloch states momentum space. Based on metric-curvature correspondence, time-resolved angle-resolved photoemission spectroscopy experiment is measure violation of spectral sum rule caused by pulse electric field detect metric, from which properties system may be extracted.