From Entanglement Generated Dynamics to the Gravitational Anomaly and Chiral Central Charge

We apply modular flow-entanglement generated dynamics-to characterize quantum orders of ground state wave functions. 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.