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arXiv:2008.06154 · Physical review. D/Physical review. D.

Entanglement measures for nonconformal D-branes

Arindam Lala

Published Dec 28, 2020• 15 citations
arXivHTMLPDF

Abstract

We study various entanglement measures associated with certain nonconformal field theories. We consider nonconformal $\mathrm{D}p$-brane backgrounds, which are dual to these field theories, for our holographic analysis. Restricting our interests in $p=1$, 2, 4, we explicitly compute properties of holographic entanglement entropy and the entanglement wedge cross section, ${\mathrm{E}}_{W}$, corresponding to two parallel strip shaped boundary subregions in these setups. We study low and high temperature behaviors of these quantities analytically as well as by using numerical methods. In all cases, the ${\mathrm{E}}_{W}$ decreases monotonically with temperature. We observe discontinuous jumps in ${\mathrm{E}}_{W}$, while the width of (as well as the separation between) the subregions reaches critical values in all the cases considered. However, the corresponding holographic mutual information ${\mathtt{I}}_{M}$ continuously decreases to zero for the aforementioned configurations. We also notice that the conjectured inequality ${\mathrm{E}}_{W}\ensuremath{\ge}{\mathtt{I}}_{M}/2$ still holds for nonconformal field theories as well. We analytically determine the critical separation between these subregions that triggers a phase transition in the holographic mutual information.

DOI
10.1103/physrevd.102.126026

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We evaluate reflected entropy in certain anisotropic boundary theories dual to nonrelativistic geometries using holography. It is proposed that this quantity is proportional to the minimal area of the entanglement wedge cross section. Using this prescription, we study in detail the effect of anisotropy on reflected entropy and other holographic entanglement measures. In particular, we study the discontinuous phase transition of this quantity for a symmetric configuration consisting of two disjoint strips. We find that in the specific regimes of the parameter space the critical separation is an increasing function of the anisotropy parameter and hence the correlation between the subregions becomes more pronounced. We carefully examine how these results are consistent with the behavior of other correlation measures including the mutual information. Finally, we show that the structure of the universal terms of entanglement entropy is corrected depending on the orientation of the entangling region with respect to the anisotropic direction.
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Abstract We evaluate the entanglement wedge cross section (EWCS) in asymptotically AdS geometries which are dual to boundary excited states. We carry out a perturbative analysis for calculating EWCS between the vacuum and other states for a symmetric configuration consisting of two disjoint strips and obtain analytical results in the specific regimes of the parameter space. In particular, when the states described by purely gravitational excitations in the bulk we find that the leading correction to EWCS is negative and hence the correlation between the boundary subregions decreases. We also study other types of excitations upon adding the extra matter fields including current and scalar condensate. Our study reveals some generic properties of boundary information measures dual to EWCS, e.g., entanglement of purification, logarithmic negativity and reflected entropy. Finally, we discuss how these results are consistent with the behavior of other correlation measures including the holographic mutual information.
We study mixed state entanglement measures in a higher dimensional T T ¯ deformed field theory at finite temperature. The holographic dual is described by AdS d + 1 black brane geometry with a finite cutoff. We compute the entanglement wedge cross section (EWCS), proposed to be dual to entanglement of purification and holographic entanglement negativity (HEN) for striplike subsystems. The behavior of EWCS and HEN is studied across different regimes of temperature and deformation parameter. It is observed that the deformation and temperature exhibit similar effects on these two entanglement measures. Increasing the deformation leads to a decrease in the entanglement between the subsystems.