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

TL;DR

This paper explores how modular flow, a concept from entanglement dynamics, can characterize quantum orders and relate to gravitational anomalies and chiral central charge in various quantum field theories and models.

Contribution

It demonstrates the application of modular flow to (1+1)D conformal field theories and (2+1)D gapped states, linking entanglement dynamics to gravitational anomalies and edge chiral central charge.

Findings

Modular flow relates to the chiral central charge in (1+1)D CFTs.

In (2+1)D gapped states, it supports a formula for edge chiral central charge.

Numerical results on free fermion models support the proposed picture.

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.