Entanglement Entropy from a Holographic Viewpoint

Abstract

The entanglement entropy has been historically studied by many authors in order to obtain quantum mechanical interpretations of the gravitational entropy. The discovery of AdS/CFT correspondence leads to the idea of holographic entanglement entropy, which is a clear solution to this important problem in gravity. In this article, we would like to give a quick survey of recent progresses on the holographic entanglement entropy. We focus on its gravitational aspects, so that it is comprehensible to those who are familiar with general relativity and basics of quantum field theory.

Latex, 30 pages, invited review for Classical and Quantum Gravity, minor corrections

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• Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
• Surface/State Correspondence as a Generalized Holography
• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Holographic Charged Renyi Entropies
• Quantum Entanglement of Localized Excited States at Finite Temperature
• Dynamics of Entanglement Entropy from Einstein Equation
• On short interval expansion of Rényi entropy
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• Entanglement of Local Operators in large N CFTs
• Geometric Aspects of Holographic Bit Threads
• A universal feature of CFT Renyi entropy
• Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy
• Entanglement Entropy for Singular Surfaces
• Holographic Models for Theories with Hyperscaling Violation
• Holographic Quantum Entanglement Negativity
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• Twist operators in higher dimensions
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• Holographic Entanglement Entropy in P-wave Superconductor Phase Transition
• Entropic Counterpart of Perturbative Einstein Equation
• Holographic Geometry of cMERA for Quantum Quenches and Finite Temperature
• Universal corner entanglement from twist operators
• de Sitter extremal surfaces
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• Entanglement negativity, Holography and Black holes
• Exact and Numerical Results on Entanglement Entropy in (5+1)-Dimensional CFT
• Holographic thermalization with Lifshitz scaling and hyperscaling violation
• Renormalized entanglement entropy
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• Holographic Entanglement Entropy Close to Quantum Phase Transitions
• On shape dependence of holographic mutual information in AdS4
• Charged Entanglement Entropy of Local Operators
• Backreacting p-wave Superconductors
• Characterization of Quantum Phase Transition using Holographic Entanglement Entropy
• A Holographic Proof of Rényi Entropic Inequalities
• Impact of quantum entanglement on spectrum of cosmological fluctuations
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• Charged Renyi entropies and holographic superconductors
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• Covariant holographic entanglement negativity for disjoint intervals in $Ad{S}_3/CF{T}_2$
• Holographic entanglement entropy in nonlocal theories
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• Universal entanglement for higher dimensional cones
• Entanglement Entropy of Extremal BTZ
• Constraints on RG Flows from Holographic Entanglement Entropy
• Holographic Rényi Entropies at Finite Coupling
• Quantum Entanglement of Fermionic Local Operators
• de Sitter space and extremal surfaces for spheres
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• On $d{S}_4$ extremal surfaces and entanglement entropy in some ghost CFTs
• Holographic Rényi entropy in AdS${}_3$/LCFT${}_2$ correspondence
• Linear growth of entanglement entropy in holographic thermalization captured by horizon interiors and mutual information
• Cosmological spectrum of two-point correlation function from vacuum fluctuation of Stringy Axion field in De Sitter space: A study of the role of Quantum Entanglement
• Holographic entanglement entropy in the nonconformal medium
• Entanglement thermodynamics for non-conformal D-branes
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• Charged Topological Entanglement Entropy
• Holographic Entanglement Negativity for Conformal Field Theories with a Conserved Charge
• Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
• Holographic entanglement density for spontaneous symmetry breaking
• Entanglement Entropy in Holographic P-Wave Superconductor/Insulator Model
• On one-loop entanglement entropy of two short intervals from OPE of twist operators
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• Looking at Shadows of Entanglement Wedges
• Holographic Entanglement Entropy of Mass-deformed ABJM Theory
• Evolutions of entanglement and complexity after a thermal quench in massive gravity theory
• Evolution of Entanglement Entropy in Orbifold CFTs
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• Informational properties for Einstein-Maxwell-Dilaton Gravity
• An Inverse Mass Expansion for Entanglement Entropy in Free Massive Scalar Field Theory
• Informational properties of holographic Lifshitz field theory
• A note on the AdS/CFT correspondence and the nature of spacetime in quantum gravity
• de Sitter versus anti-de Sitter in Horndeski-like gravity
• More on Phase Transition and Renyi Entropy
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• Holographic entanglement entropy in imbalanced superconductors
• Holographic Entanglement Entropy of Anisotropic Minimal Surfaces in LLM Geometries
• Complexity growth of massive black hole with a probe string
• Entanglement Wedge Cross Section with Gauss-Bonnet Corrections and Thermal Quench
• Holographic Calculation of BMSFT Mutual and 3-partite Information
• Holographic entanglement entropy and entanglement thermodynamics of `black' non-susy D3 brane
• Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization
• Entanglement Entropy and Duality in AdS(4)
• Lattice QCD study of static quark and antiquark correlations via entanglement entropies
• Static Elliptic Minimal Surfaces in AdS(4)
• Mixed state entanglement in deformed field theory at finite temperature
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• Entangled spins and ghost-spins
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• Charge transport properties in a novel holographic quantum phase transition model
• On the Holographic Entanglement Entropy for Non-smooth Entangling Curves in AdS(4)
• Measuring multipartite quantum correlations by thermodynamic work extraction
• Lattice QCD study of static quark and antiquark correlations at finite $T$ via entanglement entropies
• Holographic RG flow triggered by a classically marginal operator
• Entanglement at the Soft-Hair Horizon
• Scalar filed evolution and area spectrum for Lovelock-AdS black holes
• QCD, with Strings Attached
• Quantum correlation in quark-gluon medium
• HEE and HSC for flavors: perturbative structure in open string geometries
• How is the Presence of Horizons and Localized Matter Encoded in the Entanglement Entropy?
• Holographic entanglement negativity for disjoint subsystems in $\mathrm{Ad}{\mathrm{S}}_{\mathrm{d}+1}/CF{\mathrm{T}}_{\mathrm{d}}$
• Diagnosing quantum phase transition via holographic entanglement entropy at finite temperature
• Holographic entanglement negativity for a single subsystem in conformal field theories with a conserved charge
• D5-brane in AdS black holes with nonzero gauge flux
• Entanglement Entropy of Compactified Branes and Phase Transition