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Register a new userEntanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench
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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.
We present a new class of local quenches described by mixed states, parameterized universally by two parameters. We compute the evolutions of entanglement entropy for both a holographic and Dirac fermion CFT in two dimensions. This turns out to be equivalent to calculations of two point functions on a torus. We find that in holographic CFTs, the results coincide with the known results of pure state local operator quenches. On the other hand, we obtain new behaviors in the Dirac fermion CFT, which are missing in the pure state counterpart. By combining our results with the inequalities known for von-Neumann entropy, we obtain an upper bound of the pure state local operator quenches in the Dirac fermion CFT. We also explore predictions about the behaviors of entanglement entropy for more general mixed states.
We study the entanglement wedge cross-section (EWCS) in holographic Aether gravity theory, a gravity theory with Lorentz symmetry breaking meanwhile keeping the general covariance intact. We find that only a limited parameter space is allowed to obtain a black brane with positive Hawking temperature. Subject to these allowed parameter regions, we find that the EWCS could exhibit non-monotonic behaviors with system parameters. Meanwhile, the holographic entanglement entropy (HEE), and the corresponding mutual information (MI), can only exhibit monotonic behaviors. These phenomena suggest that the EWCS could capture much more rich content of the entanglement than that of the HEE and the MI. The role of the Lorentz violation in determining the behaviors of quantum information-related quantities is also analyzed.
We study the mixed state entanglement properties in two holographic axion models by examining the behavior of the entanglement wedge minimum cross section (EWCS), and comparing it with the holographic entanglement entropy (HEE) and mutual information (MI). We find that the behavior of HEE, MI and EWCS with Hawking temperature is monotonic, while the behavior with the axion parameter $k$ is more rich, which depends on the size of the configuration and the values of the other two parameters. Interestingly, the EWCS monotonically increases with the coupling constant $kappa$ between the axion field and the Maxwell field, while HEE and MI can be non-monotonic. It suggests that the EWCS, as a mixed state entanglement measure, captures distinct degrees of freedom from the HEE and MI indeed. We also provide analytical understandings for most of the numerical results.
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