Entanglement entropy: Holography and renormalization group

2018/01/31 by Tatsuma Nishioka · 288 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Cosmology and Gravitation Theories #Entropy (arrow of time) #Geometry #Joint quantum entropy #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum discord #Quantum entanglement #Quantum field theory #Quantum mechanics #Quantum relative entropy #Renormalization group #Squashed entanglement #Theoretical physics #hep-th

paper · pdf · doi:10.1103/revmodphys.90.035007

published in Reviews of Modern Physics 90(3) (American Physical Society) · 61 pages, An invited review, Submitted to Reviews of Modern Physics, v2: typos corrected, references added, v3: a typo corrected

openalex publication_date 2018/09/17 · arxiv created 2019/12/25 · arxiv updated 2019/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this review the entanglement and Renyi entropies in quantum field theory are described from different points of view, including the perturbative approach and holographic dualities. The applications of these results to constraining renormalization group flows are presented effectively and illustrated with a variety of examples.

Citations

• Colloquium: Area laws for the entanglement entropy
• Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
• Cool horizons for entangled black holes
• The Large-N Limit of Superconformal Field Theories and Supergravity
• Quantum entanglement

Cited by

• Thermal and chemical response from entanglement entropy
• Criticality on Rényi defects at (2+1)d O(3) quantum critical points
• Entanglement Entropy in Closed String Theory
• Quantum entanglement within quarkonium
• Measuring Rényi entropy using a projected Loschmidt echo
• Symmetry resolved entanglement in Lifshitz field theories
• Quantum entanglement between partons in a strongly coupled quantum field theory
• Probing chiral topological states with permutation defects
• Geometric Rényi mutual information induced by localized particle excitations in quantum field theory
• Symmetry-Resolved Entanglement Entropy from Heat Kernels
• Convex semidefinite tensor optimization and quantum entanglement
• Characterizing the initial state of hydrodynamics in pp and pA collisions
• Notes on Some Entanglement Properties of Quantum Field Theory
• Entanglement Spectrum Resolved by Loop Symmetries
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
• Aspects of holographic entanglement using physics-informed-neural-networks
• Holographic defect CFTs with Dirichlet end-of-the-world branes
• Entanglement Entropy and Thermodynamics of Dynamical Black Holes
• Timelike Entanglement Entropy in Higher Curvature Gravity
• Boundary Renormalization Group Flow of Entanglement Entropy at a (2+1)-Dimensional Quantum Critical Point
• Finite entropy sums in quantum field theory
• Comments on Defining Entanglement Entropy
• Multipartite entanglement from ditstrings for 1+1D systems
• Quantum Entanglement in Time
• Twist operators and pseudo entropies in two-dimensional momentum space
• Symmetry-based theory of Dirac fermions on two-dimensional hyperbolic crystals: Coupling to the spin connection
• Lectures on entanglement entropy in field theory and holography
• Quantum entanglement in cosmology
• The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes
• Momentum space entanglement of four fermion field theory
• Hyperscaling of Fidelity and Operator Estimations in the Critical Manifold
• Detector Based Evaluation of Extractable Entanglement in Flat spacetime
• Finite Cut-Off Holography and the DBI Counter-Term
• Capacity of Entanglement in Lifshitz Theories
• Rethinking quantum information in gravity and fields
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Entanglement susceptibilities and universal geometric entanglement entropy
• Kaluza–Klein gravity and cosmology emerging from G. Perelman’s entropy functionals and quantum geometric information flows
• Typical and extreme entropies of long-lived isolated quantum systems
• The strong CP problem, general covariance, and horizons
• Page curve like dynamics in Interacting Quantum Systems
• Global aspects of conformal symmetry and the ANEC in dS and AdS
• Inverted c-functions in thermal states
• The ℏ→ 0 Limit of the Entanglement Entropy
• c-theorem of the entanglement entropy
• Particle number fluctuations, Rényi entropy, and symmetry-resolved entanglement entropy in a two-dimensional Fermi gas from multidimensional bosonization
• Inhomogeneous entanglement structure in monoaxial chiral ferromagnetic quantum spin chain
• Position dependence of the holographic entanglement entropy for an accelerating quark-antiquark pair
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Entanglement and Non-Locality in Quantum Protocols with Identical Particles. [europepmc]
• Scaling Limits of Lattice Quantum Fields by Wavelets. [europepmc]
• Measuring entanglement entropy and its topological signature for phononic systems. [europepmc]
• Realizing the entanglement Hamiltonian of a topological quantum Hall system. [europepmc]

Related

• Holographic entanglement entropy and renormalization group flow
• Lectures on entanglement entropy in field theory and holography
• Holographic Entanglement Entropy: An Overview
• Holographic entanglement entropy beyond coherent states
• Entanglement Entropy and The Density Matrix Renormalization Group