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

• URL: http://arxiv.org/abs/2206.02823v1
• Date: Mon, 6 Jun 2022 18:01:28 GMT
• Title: From entanglement generated dynamics to the gravitational anomaly and chiral central charge
• Authors: Ruihua Fan
• Abstract summary: 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. Next, we apply it to (2+1)D gapped ground states where it reduces to a recently proposed formula.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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