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

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 نشر من قبل Yuya Kusuki
 تاريخ النشر 2019
  مجال البحث فيزياء
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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.



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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 RCFTs. Our results directly suggest the classical correlation also plays an important role in the subregion/subregion duality even for dynamical setup. Besides a local operator quench, we study the reflected entropy in a heavy state and provide improved bulk interpretation. 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.
The entanglement wedge cross section (EWCS) is numerically investigated both statically and dynamically in a five-dimension AdS-Vaidya spacetime with Gauss-Bonnet (GB) corrections, focusing on two identical rectangular strips on the boundary. In the static case, EWCS arises as the GB coupling constant $alpha$ increasing, and disentangles at smaller separations between two strips for smaller $alpha$. For the dynamical case we observe that the monotonic relation between EWCS and $alpha$ holds but the two strips no longer disentangle monotonically. In the early stage of thermal quenching, when disentanglement occurs, the smaller $alpha$, the greater separations. As time evolving, two strips then disentangle at larger separations with larger $alpha$. Our results suggest that the higher order derivative corrections also have nontrivial effects on the EWCS, so do on the entanglement of purification in the dual boundary theory.
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