Replica wormhole geometries justify the replica trick computation of the Page curve in holographic black hole models and support entanglement wedge reconstruction via the Petz map.
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Entanglement entropy and conformal field theory
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abstract
We review the conformal field theory approach to entanglement entropy. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries, and the case of several disjoint intervals. We discuss the behaviour away from the critical point and the spectrum of the reduced density matrix. Quantum quenches, as paradigms of non-equilibrium situations, are also considered.
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representative citing papers
Hawking radiation entropy follows the Page curve when quantum extremal surfaces are identified with RT/HRT surfaces in a higher-dimensional holographic dual, making the black hole interior part of the radiation's entanglement wedge.
The derivative of entanglement entropy with respect to subregion volume equals the thermal entropy density in the large-subregion limit, verified via lattice simulations of the finite-density O(4) model using dual worm algorithms.
The stabilizer Rényi entropy at Rényi index 1/2 for the finite-temperature transverse-field Ising chain reduces exactly to a Pfaffian whose universal scaling function is a level-eight eta quotient encoding hidden defect-like conformal boundary data.
In large-central-charge holographic CFTs, post-quench mutual information organizes into six phases governed by conformal block dominance and D4 symmetry breaking to Z2 x Z2.
Crosscap defects are introduced in CFTs via Z2 quotients, with crossing equations derived and CFT data computed in the O(N) model at Gaussian and Wilson-Fisher points showing absent displacement and tilt operators for generic p.
Self-interactions in scalar and gauge theories suppress gravitational particle production in a quench modeling cosmic expansion, as computed with tensor networks.
An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.
In a 2d evaporating black hole model, large boosts create O(1/G_N) gradients in bulk entropy that move the quantum extremal surface, causing the generalized entropy to follow unitary expectations with information disappearing after a scrambling time and a phase transition at the Page time.
Complexified exactly-marginal couplings produce solvable complex CFTs, with the Ising defect verified numerically in non-Hermitian chains.
Proposes an exact kinematic sector in AdS/CFT using Weyl-frame CFT on open solid torus, treating AdS as kinematic geometry recovered only in singular limits, with two-point functions defining entanglement entropy without replicas.
Entangling power in Heisenberg spin chains shows a monotonic decrease with growing symmetry in small models, sharp dips at SU(2) and free-fermion points in finite chains, and vanishes at SU(2) points but maximizes at the free-fermion point in the thermodynamic limit for the S-matrix.
Uniform MPS simulations of dense 1+1D SU(2) gauge theory find Tomonaga-Luttinger liquid infrared behavior with central charge 1, density modulations at the predicted wavenumber, and a smooth crossover in the Luttinger parameter from K~1 to K~1/2 that realizes the quarkyonic picture with coexisting q
Entanglement revivals in evaporating black holes survive only when radiation intervals are larger than a critical length set by the exponential of the black-hole scrambling time.
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Derives heavy-light conformal blocks in 2d C/G CFTs and computes excited-state entanglement entropy via replica trick, finding thermal form that reproduces holographic EE and establishes dictionary between boundary weights and bulk mass/angular momentum.
Proves stabilizer-Shannon Renyi equivalence for Gaussian states, enabling exact results and CFT scalings for stabilizer entropies in critical free-fermion chains.
Holographic models of interface CFTs connect the effective central charge in entanglement entropy to a limiting case of boundary entropy, while adding finite terms for non-crossing intervals to satisfy strong subadditivity.
Proves exact separability for disconnected subsystems in dimer RK states and exponentially suppressed entanglement for RVB states on arbitrary lattices, with negativity expressed via partition functions.
Fuzzball models with stretched horizons modify or eliminate entanglement islands depending on boundary conditions and cap geometry, producing information paradox analogues in some cases.
A central-charge Rényi entropy is constructed via the CHM map in a grand canonical ensemble with fixed charge, volume, and central charge potential, shown to obey Rényi inequalities and to separate theory space into dominant-theory and multi-theory regimes at a characteristic index n*.
Genuine multi-entropy in heavy local quenches in 2D holographic CFTs is kinematically fixed to logarithms of rational functions of time, independent of heavy operator dimension, due to global saddle selection in the geodesic network.
Tensor network calculation of magic and entanglement in SU(2) lattice gauge theory ground state shows a crossover from magic-rich to less-magic regime at g_star.
The study uncovers symmetry-protected topological phases with coexisting spontaneous symmetry breaking in the triangular Majorana-Hubbard ladder model of interacting Majorana fermions.
citing papers explorer
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Replica wormholes and the black hole interior
Replica wormhole geometries justify the replica trick computation of the Page curve in holographic black hole models and support entanglement wedge reconstruction via the Petz map.
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The Page curve of Hawking radiation from semiclassical geometry
Hawking radiation entropy follows the Page curve when quantum extremal surfaces are identified with RT/HRT surfaces in a higher-dimensional holographic dual, making the black hole interior part of the radiation's entanglement wedge.
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Determination of thermodynamics from entanglement entropy in the finite-density O(N) model
The derivative of entanglement entropy with respect to subregion volume equals the thermal entropy density in the large-subregion limit, verified via lattice simulations of the finite-density O(4) model using dual worm algorithms.
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Hidden Conformal Boundary Data in Finite-Temperature Stabilizer Entropy
The stabilizer Rényi entropy at Rényi index 1/2 for the finite-temperature transverse-field Ising chain reduces exactly to a Pfaffian whose universal scaling function is a level-eight eta quotient encoding hidden defect-like conformal boundary data.
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Dynamical Entanglement Phase Transitions in Holographic CFTs
In large-central-charge holographic CFTs, post-quench mutual information organizes into six phases governed by conformal block dominance and D4 symmetry breaking to Z2 x Z2.
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Crosscap Defects
Crosscap defects are introduced in CFTs via Z2 quotients, with crossing equations derived and CFT data computed in the O(N) model at Gaussian and Wilson-Fisher points showing absent displacement and tilt operators for generic p.
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Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states
Self-interactions in scalar and gauge theories suppress gravitational particle production in a quench modeling cosmic expansion, as computed with tensor networks.
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Symmetry-Resolved Entanglement Entropy from Heat Kernels
An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.
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The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
In a 2d evaporating black hole model, large boosts create O(1/G_N) gradients in bulk entropy that move the quantum extremal surface, causing the generalized entropy to follow unitary expectations with information disappearing after a scrambling time and a phase transition at the Page time.
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Complex Conformal Manifolds
Complexified exactly-marginal couplings produce solvable complex CFTs, with the Ising defect verified numerically in non-Hermitian chains.
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Exact Holographic Kinematics in AdS/CFT
Proposes an exact kinematic sector in AdS/CFT using Weyl-frame CFT on open solid torus, treating AdS as kinematic geometry recovered only in singular limits, with two-point functions defining entanglement entropy without replicas.
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Entangling Power: A Probe of Symmetry and Integrability in Quantum Many-Body Systems
Entangling power in Heisenberg spin chains shows a monotonic decrease with growing symmetry in small models, sharp dips at SU(2) and free-fermion points in finite chains, and vanishes at SU(2) points but maximizes at the free-fermion point in the thermodynamic limit for the S-matrix.
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Dense $\mathrm{QC_2D_2}$ with uniform matrix product states
Uniform MPS simulations of dense 1+1D SU(2) gauge theory find Tomonaga-Luttinger liquid infrared behavior with central charge 1, density modulations at the predicted wavenumber, and a smooth crossover in the Luttinger parameter from K~1 to K~1/2 that realizes the quarkyonic picture with coexisting q
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Entanglement Revivals and Scrambling for Evaporating Black Holes
Entanglement revivals in evaporating black holes survive only when radiation intervals are larger than a critical length set by the exponential of the black-hole scrambling time.
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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Conformal Blocks in 2d Carrollian/Galilean CFTs and Excited State Entanglement Entropy
Derives heavy-light conformal blocks in 2d C/G CFTs and computes excited-state entanglement entropy via replica trick, finding thermal form that reproduces holographic EE and establishes dictionary between boundary weights and bulk mass/angular momentum.
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Stabilizer-Shannon Renyi Equivalence: Exact Results for Quantum Critical Chains
Proves stabilizer-Shannon Renyi equivalence for Gaussian states, enabling exact results and CFT scalings for stabilizer entropies in critical free-fermion chains.
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Connecting boundary entropy and effective central charge at holographic interfaces
Holographic models of interface CFTs connect the effective central charge in entanglement entropy to a limiting case of boundary entropy, while adding finite terms for non-crossing intervals to satisfy strong subadditivity.
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Separability and entanglement of resonating valence-bond states
Proves exact separability for disconnected subsystems in dimer RK states and exponentially suppressed entanglement for RVB states on arbitrary lattices, with negativity expressed via partition functions.
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Entanglement islands, fuzzballs and stretched horizons
Fuzzball models with stretched horizons modify or eliminate entanglement islands depending on boundary conditions and cap geometry, producing information paradox analogues in some cases.
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Extended Thermodynamics and Renyi Entropy Beyond Fixed Central Charge
A central-charge Rényi entropy is constructed via the CHM map in a grand canonical ensemble with fixed charge, volume, and central charge potential, shown to obey Rényi inequalities and to separate theory space into dominant-theory and multi-theory regimes at a characteristic index n*.
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Multi-entropy in heavy local quenches
Genuine multi-entropy in heavy local quenches in 2D holographic CFTs is kinematically fixed to logarithms of rational functions of time, independent of heavy operator dimension, due to global saddle selection in the geodesic network.
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Magic and entanglement in 1+1-dimensional SU(2) lattice gauge theory
Tensor network calculation of magic and entanglement in SU(2) lattice gauge theory ground state shows a crossover from magic-rich to less-magic regime at g_star.
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Symmetry-Protected Topological Phases in the Triangular Majorana-Hubbard Ladder
The study uncovers symmetry-protected topological phases with coexisting spontaneous symmetry breaking in the triangular Majorana-Hubbard ladder model of interacting Majorana fermions.
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Timelike entanglement entropy Revisited
An operator-algebraic definition of timelike entanglement entropy in QFT is shown to be real-valued via the timelike tube theorem.
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Imprints of dynamical phases in semiclassical entanglement entropy in 2D CFT
Semiclassical entanglement entropy in driven 2D CFT states exhibits dynamical phase imprints; the holographic backreacted minimal area matches the CFT result at O(c^0) and verifies the FLM conjecture.
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Lectures on Semiclassical Methods for Composite Operators
Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.
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Lecture notes on strings in AdS$_3$ from the worldsheet and the AdS$_3$/CFT$_2$ duality
Lecture notes deliver a self-contained pedagogical overview of worldsheet strings in AdS3 with NSNS flux, summarizing 25 years of results with emphasis on spectrally flowed correlation functions.
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Lectures on entanglement entropy in field theory and holography
Lecture notes surveying entanglement entropy in QFT and holography, emphasizing physical aspects and the Ryu-Takayanagi formula.
- Large-c BCFT Entanglement Entropy with Deformed Boundaries from Emergent JT Gravity