[Paper Review] Holographic Study of Entanglement of Purification for Excited States

Mohammad Sahraei, Mohammad Javad Vasli+2 more|arXiv (Cornell University)|May 27, 2021

Black Holes and Theoretical Physics51 references4 citations

TL;DR

This paper uses holographic duality to compute the entanglement of purification (EoP) for excited states in AdS spacetimes, showing that EoP decreases under gravitational and scalar condensate excitations when the operator dimension satisfies the unitarity bound. The minimal cross-sectional area of the entanglement wedge provides a geometric measure of EoP, revealing reduced correlations in excited states compared to the vacuum.

ABSTRACT

We evaluate the entanglement of purification (EoP), which measures correlations between two subsystems, for excited states dual to asymptotically AdS spacetimes using holography. In this framework EoP is given by the minimal cross sectional area of an entanglement wedge. We carry out a perturbative analysis for calculating EoP 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 EoP is negative and the correlation between the subregions decreases. We also study other types of excitations upon adding the extra matter fields including current and scalar condensate. For the latter class of excitations, we find that the variation of EoP is negative, when the dimension of the scalar operator respects the unitarity bound. Finally, we discuss how these results are consistent with the behavior of other correlation measures including the holographic mutual information.

Motivation & Objective

• To investigate how entanglement of purification (EoP) changes in excited states dual to asymptotically AdS spacetimes using holography.
• To understand the behavior of EoP under various bulk excitations, including gravitational and matter fields.
• To determine whether EoP decreases in excited states, particularly when the scalar operator dimension respects the unitarity bound.
• To compare the variation of EoP with other correlation measures such as holographic mutual information.

Proposed method

• Employing the holographic entanglement wedge cross-section as the geometric dual to EoP in AdS/CFT.
• Performing a perturbative analysis around the vacuum state for a symmetric configuration of two disjoint strips.
• Calculating the leading-order correction to EoP using linearized gravity and matter field excitations in the bulk.
• Including current and scalar condensate fields to study their impact on EoP variation.
• Using the minimal area prescription to compute EoP in the presence of bulk excitations.
• Analyzing the parameter space to identify regimes where analytical results for EoP corrections are obtainable.

Experimental results

Research questions

• RQ1 How does the entanglement of purification change in excited states dual to asymptotically AdS spacetimes under purely gravitational excitations?
• RQ2 What is the sign and magnitude of the leading-order correction to EoP when scalar condensates are introduced in the bulk?
• RQ3 Does the variation of EoP remain negative when the scalar operator dimension lies within the unitarity bound?
• RQ4 How does the behavior of EoP compare to that of holographic mutual information in excited states?
• RQ5 Under what conditions does EoP decrease, and what does this imply about correlations between subsystems?

Key findings

• The leading correction to EoP is negative when the excited state is described by purely gravitational bulk excitations, indicating reduced correlations between the subsystems.
• For scalar condensate excitations, the variation of EoP is negative when the scalar operator dimension satisfies the unitarity bound.
• The decrease in EoP is consistent with the behavior of other correlation measures such as holographic mutual information.
• Analytical results for EoP corrections are obtained in specific regimes of the parameter space using perturbative methods.
• The minimal cross-sectional area of the entanglement wedge provides a reliable geometric measure of EoP in the studied configurations.