Dynamics of entanglement wedge cross section from conformal field theories

We derive dynamics of the entanglement wedge cross section directly from the two-dimensional holographic CFTs with a local operator quench. This derivation is based on the reflected entropy, a correlation measure for mixed states. We further compare these results with the mutual information and ones for integrable systems. This comparison directly suggests the classical correlation plays an important role in chaotic systems, unlike integrable ones. Besides a local operator quench, we study the reflected entropy in heavy primary states and find a breaking of the subsystem ETH. We checked the above results also hold for the odd entanglement entropy, which is another measure for mixed states related to the entanglement wedge cross section. (C) 2021 The Authors. Published by Elsevier B.V.

Automated summary

The dynamics of entanglement wedge cross section is derived directly from two-dimensional holographic CFTs with a local operator quench, based on the reflected entropy. The comparison with mutual information and results for integrable systems suggests classical correlation plays an important role in chaotic systems. Additionally, a study on the reflected entropy in heavy primary states shows a breaking of the subsystem ETH, and results were also confirmed for odd entanglement entropy.