Enhanced corrections near holographic entanglement transitions: a chaotic case study

Abstract

Recent work found an enhanced correction to the entanglement entropy of a subsystem in a chaotic energy eigenstate. The enhanced correction appears near a phase transition in the entanglement entropy that happens when the subsystem size is half of the entire system size. Here we study the appearance of such enhanced corrections holographically. We show explicitly how to find these corrections in the example of chaotic eigenstates by summing over contributions of all bulk saddle point solutions, including those that break the replica symmetry. With the help of an emergent rotational symmetry, the sum over all saddle points is written in terms of an effective action for cosmic branes. The resulting Renyi and entanglement entropies are then naturally organized in a basis of fixed-area states and can be evaluated directly, showing an enhanced correction near holographic entanglement transitions. We comment on several intriguing features of our tractable example and discuss the implications for finding a convincing derivation of the enhanced corrections in other, more general holographic examples.

arXiv comment36 pages, 9 figures

References in corpus (15)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Covariant Holographic Entanglement Entropy Proposal
• Replica Wormholes and the Entropy of Hawking Radiation
• Entanglement Renyi entropies in holographic theories
• The Gravity Dual of Renyi Entropy
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
• Subsystem ETH
• Flat entanglement spectra in fixed-area states of quantum gravity
• Holographic Renyi Entropy from Quantum Error Correction
• Renyi Entropy of Chaotic Eigenstates
• Structure of chaotic eigenstates and their entanglement entropy
• Universal eigenstate entanglement of chaotic local Hamiltonians
• One-loop universality of holographic codes
• Holographic Renyi Entropy at High Energy Density

Cited by in corpus (40)

• Bra-ket wormholes in gravitationally prepared states
• Observations of Hawking radiation: the Page curve and baby universes
• A violation of global symmetries from replica wormholes and the fate of black hole remnants
• Replica wormholes for an evaporating 2D black hole
• Quantum Information in Holographic Duality
• Leading order corrections to the quantum extremal surface prescription
• Holographic entanglement negativity and replica symmetry breaking
• Signatures of global symmetry violation in relative entropies and replica wormholes
• Real-time gravitational replicas: Formalism and a variational principle
• Reflected entropy in random tensor networks
• Probing phase transitions of holographic entanglement entropy with fixed area states
• The Page Curve for Reflected Entropy
• Relative Entropy of Random States and Black Holes
• Replica Wormholes and Holographic Entanglement Negativity
• Distinguishing Random and Black Hole Microstates
• Islands with Gravitating Baths: Towards ER = EPR
• Complexity and entanglement in non-local computation and holography
• Entanglement transitions as a probe of quasiparticles and quantum thermalization
• Reflected entropy in random tensor networks II: a topological index from the canonical purification
• Crosscap States in Integrable Field Theories and Spin Chains
• Mixed-state entanglement and information recovery in thermalized states and evaporating black holes
• An Alternative Method for Extracting the von Neumann Entropy from Renyi Entropies
• Beyond islands: A free probabilistic approach
• A Modified Cosmic Brane Proposal for Holographic Renyi Entropy
• The Spacetime Geometry of Fixed-Area States in Gravitational Systems
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Aspects of Holography in Conical $Ad{S}_3$
• Entanglement Negativity and Replica Symmetry Breaking in General Holographic States
• Modular parallel transport of multiple intervals in 1+1-dimensional free fermion theory
• Minimal Areas from Entangled Matrices
• Subsystem entropy in 2d CFT and KdV ETH
• Large and Small Corrections to the JLMS Formula from Replica Wormholes
• Negative R$\acute{\text{e}}$nyi entropy and Brane intersection
• Counting atypical black hole microstates from entanglement wedges
• The area operator and fixed area states in conformal field theories
• Spinning Particle Geometries in AdS${}_3$/CFT${}_2$
• The Markov gap for geometric reflected entropy
• A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture)
• Euclidean and complex geometries from real-time computations of gravitational Rényi entropies
• Spectral Projections for Density Matrices in Quantum Field Theories