From entanglement generated dynamics to the gravitational anomaly and chiral central charge

Abstract

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.

Time Expansion at the Interface of Organic Metallic Surfaces

“…The process is also related to entanglement in the ground state wave functions 30 . The findings and theory above correlates with the description of accumulation of the accesses positive charge as function of decreasing temperature in the experimental part of this paper and the chiral current given rise to the large magnetic field observed.…”