Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench

TL;DR

This paper explores the dynamics of the entanglement wedge cross section via reflected entropy in holographic CFTs following local operator quenches, revealing insights into chaos, correlations, and bulk interpretation.

Contribution

It introduces a detailed analysis of reflected and odd entanglement entropy dynamics, including quantum corrections and technical advancements in the replica trick methodology.

Findings

Reflected entropy diagnoses chaos in mixed states.

Reflected entropy characterizes classical correlations in subregion duality.

Derived consistent results from odd entanglement entropy.

Abstract

We derive dynamics of the entanglement wedge cross section from the reflected entropy for local operator quench states in the holographic CFT. By comparing between the reflected entropy and the mutual information in this dynamical setup, we argue that (1) the reflected entropy can diagnose a new perspective of the chaotic nature for given mixed states and (2) it can also characterize classical correlations in the subregion/subregion duality. Moreover, we point out that we must improve the bulk interpretation of a heavy state even in the case of well-studied entanglement entropy. Finally, we show that we can derive the same results from the odd entanglement entropy. The present paper is an extended version of our earlier report arXiv:1907.06646 and includes many new results: non-perturbative quantum correction to the reflected/odd entropy, detailed analysis in both CFT and bulk sides, many technical aspects of replica trick for reflected entropy which turn out to be important for general setup, and explicit forms of multi-point semi-classical conformal blocks under consideration.