Holographic Entanglement Entropy: An Overview

Holographic Entanglement Entropy: An Overview

15 Jun 2009 | Tatsuma Nishioka, Shinsei Ryu, Tadashi Takayanagi
This article reviews recent progress in understanding entanglement entropy through the holographic correspondence in the AdS/CFT framework. It begins by introducing the concept of holographic entanglement entropy, which is a universal observable that can be used to probe the quantum properties of systems. The authors discuss the definition and properties of entanglement entropy in quantum field theories (QFTs) and many-body systems, emphasizing its area law behavior. They then present the holographic formula for entanglement entropy, derived from the AdS/CFT correspondence, and explain how this formula reproduces the area law and strong subadditivity properties of entanglement entropy. The article explores applications of holographic entanglement entropy to various phenomena, including confinement/deconfinement phase transitions, black hole entropy, and covariant formulations of holography. It also discusses the holographic description of entanglement entropy in higher dimensions, providing explicit results for infinite strips, disks, and wedges with cusps. The authors conclude by highlighting the importance of holographic entanglement entropy in understanding quantum many-body physics and its potential for simulating quantum states efficiently.This article reviews recent progress in understanding entanglement entropy through the holographic correspondence in the AdS/CFT framework. It begins by introducing the concept of holographic entanglement entropy, which is a universal observable that can be used to probe the quantum properties of systems. The authors discuss the definition and properties of entanglement entropy in quantum field theories (QFTs) and many-body systems, emphasizing its area law behavior. They then present the holographic formula for entanglement entropy, derived from the AdS/CFT correspondence, and explain how this formula reproduces the area law and strong subadditivity properties of entanglement entropy. The article explores applications of holographic entanglement entropy to various phenomena, including confinement/deconfinement phase transitions, black hole entropy, and covariant formulations of holography. It also discusses the holographic description of entanglement entropy in higher dimensions, providing explicit results for infinite strips, disks, and wedges with cusps. The authors conclude by highlighting the importance of holographic entanglement entropy in understanding quantum many-body physics and its potential for simulating quantum states efficiently.
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