  We apply modular flow -- entanglement generated dynamics -- to characterize
quantum orders of ground state wavefunctions. In particular, we study the
linear response of the entanglement entropy of a simply connected region with
respect to modular flow. First, we apply it to (1+1)D conformal field theories
and demonstrate its relationship to the chiral central charge -- or
equivalently the perturbative gravitational anomaly -- which is shown to
vanish. Next, we apply it to (2+1)D gapped ground states where it reduces to a
recently proposed formula by Kim et. al. that is conjectured to compute the
edge chiral central charge. Modular flow provides an intuitive picture for this
conjecture based on bulk-edge correspondence. We also provide numerics on free
fermion models that lend support to our picture.
