Remarks on the entanglement entropy for disconnected regions

Abstract

Few facts are known about the entanglement entropy for disconnected regions in quantum field theory. We study here the property of extensivity of the mutual information, which holds for free massless fermions in two dimensions. We uncover the structure of the entropy function in the extensive case, and find an interesting connection with the renormalization group irreversibility. The solution is a function on space-time regions which complies with all the known requirements a relativistic entropy function has to satisfy. We show that the holographic ansatz of Ryu and Takayanagi, the free scalar and Dirac fields in dimensions greater than two, and the massive free fields in two dimensions all fail to be exactly extensive, disproving recent conjectures.

14 pages, 4 figures, some additions

References in corpus (29)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Aspects of Holographic Entanglement Entropy
• A Covariant Holographic Entanglement Entropy Proposal
• The Role of Relative Entropy in Quantum Information Theory
• Calculation of reduced density matrices from correlation functions
• Area laws in quantum systems: mutual information and correlations
• A finite entanglement entropy and the c-theorem
• Aspects of Large N Gauge Theory Dynamics as Seen by String Theory
• Entanglement entropy, conformal invariance and extrinsic geometry
• The Conical Singularity And Quantum Corrections To Entropy Of Black Hole
• Universal terms for the entanglement entropy in 2+1 dimensions
• Proof of the Holographic Formula for Entanglement Entropy
• AdS/CFT and Strong Subadditivity of Entanglement Entropy
• Black hole entropy as entanglement entropy: a holographic derivation
• Entanglement Entropy and Twist Fields
• Algebraic Holography
• Holographic Calculation of Boundary Entropy
• Spectral Geometry and One-loop Divergences on Manifolds with Conical Singularities
• On the integrability of Wilson loops in AdS_5 x S^5: Some periodic ansatze
• Entanglement entropy of black holes and AdS/CFT correspondence
• Geometric entropy, area, and strong subadditivity
• Holographic entanglement entropy for disconnected regions
• Entanglement Entropy in Quantum Gravity and the Plateau Problem
• A note on the extensivity of the holographic entanglement entropy
• Gross-Ooguri Phase Transition at Zero and Finite Temperature: Two Circular Wilson Loop Case
• Effective actions with fixed points, (error in derivation of coefficient corrected)
• Entropy localization and extensivity in the semiclassical black hole evaporation

Cited by in corpus (149)

• Entanglement entropy and conformal field theory
• Towards a derivation of holographic entanglement entropy
• Quantum corrections to holographic entanglement entropy
• Holographic Entanglement Entropy: An Overview
• Entanglement entropy in free quantum field theory
• Holographic c-theorems in arbitrary dimensions
• Entanglement negativity in quantum field theory
• Entanglement entropy of two disjoint intervals in conformal field theory
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Holographic Mutual Information is Monogamous
• Entanglement negativity in extended systems: A field theoretical approach
• Deriving covariant holographic entanglement
• A refinement of entanglement entropy and the number of degrees of freedom
• Holographic Calculations of Renyi Entropy
• Finite temperature entanglement negativity in conformal field theory
• Universality of corner entanglement in conformal field theories
• Entanglement entropy of two disjoint blocks in XY chains
• Reduced density matrix and internal dynamics for multicomponent regions
• Entanglement entropy of two disjoint blocks in critical Ising models
• Entanglement negativity after a global quantum quench
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Some Results on Mutual Information of Disjoint Regions in Higher Dimensions
• Mutual information after a local quench in conformal field theory
• Entanglement negativity in the critical Ising chain
• Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• On reduced density matrices for disjoint subsystems
• Some Calculable Contributions to Holographic Entanglement Entropy
• Entanglement entropy and superselection sectors I. Global symmetries
• Entanglement spectrum of random-singlet quantum critical points
• Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
• Entanglement entropy of two disjoint intervals in c=1 theories
• Aspects of capacity of entanglement
• General properties of holographic entanglement entropy
• Twist operators in higher dimensions
• Entanglement entropy and negative energy in two dimensions
• Holographic entanglement entropy: near horizon geometry and disconnected regions
• Fine structure in holographic entanglement and entanglement contour
• Bit Threads and Holographic Monogamy
• Entanglement entropy of two disjoint intervals from fusion algebra of twist fields
• Universal corner entanglement from twist operators
• Observations on entanglement entropy in massive QFT's
• Entanglement negativity and conformal field theory: a Monte Carlo study
• Balanced Partial Entanglement and the Entanglement Wedge Cross Section
• Towards entanglement negativity of two disjoint intervals for a one dimensional free fermion
• Bound states and entanglement in the excited states of quantum spin chains
• Bi-partite entanglement entropy in massive 1+1-dimensional quantum field theories
• Spin structures and entanglement of two disjoint intervals in conformal field theories
• On shape dependence of holographic mutual information in AdS4
• Entanglement entropy for a Maxwell field: Numerical calculation on a two dimensional lattice
• Universal Features of Higher-Form Symmetries at Phase Transitions
• Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks
• Entanglement of Purification in Free Scalar Field Theories
• Generalizations of Reflected Entropy and the Holographic Dual
• Area terms in entanglement entropy
• Bounds on corner entanglement in quantum critical states
• Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ-> -1
• Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice
• Entanglement Entropy of Two Spheres
• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
• Balanced Partial Entanglement and Mixed State Correlations
• Real-space entanglement in the Cosmic Microwave Background
• Entanglement entropy after a partial projective measurement in $1+1$ dimensional conformal field theories: exact results
• Cornering the universal shape of fluctuations
• Measures of quantum correlations in infinite-dimensional systems
• Entanglement entropy production in gravitational collapse: covariant regularization and solvable models
• Entanglement entropy from entanglement contour: higher dimensions
• Topological Multipartite Entanglement in a Fermi Liquid
• Majorana dimers and holographic quantum error-correcting codes
• Two-cylinder entanglement entropy under a twist
• Formulas for Partial Entanglement Entropy
• Are entangled particles connected by wormholes? Support for the ER=EPR conjecture from entropy inequalities
• Positivity, entanglement entropy, and minimal surfaces
• On shape dependence of holographic entanglement entropy in AdS4/CFT3
• Local measures of entanglement in black holes and CFTs
• Generalizing the entanglement entropy of singular regions in conformal field theories
• Entanglement Structure of Deconfined Quantum Critical Points
• Relating bulk to boundary entanglement
• Entanglement of several blocks in fermionic chains
• Entropy of a subalgebra of observables and the geometric entanglement entropy
• Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains
• The entanglement and relative entropy of a chiral fermion on the torus
• On the Monogamy of Holographic $n$-partite Information
• Entanglement Entropy of Disjoint Regions in Excited States : An Operator Method
• On the Entanglement Between Interacting Scalar Field Theories
• Tripartite information of highly entangled states
• Cornering gapless quantum states via their torus entanglement
• AdS plane waves, entanglement and mutual information
• Entanglement entropy for non-coplanar regions in quantum field theory
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory -- I. Single-particle states
• Tripartite information at long distances
• Holographic entanglement entropy for perturbative higher-curvature gravities
• A Field Theory Study of Entanglement Wedge Cross Section: Odd Entropy
• A duality principle for the multi-block entanglement entropy of free fermion systems
• A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC
• All the entropies on the light-cone
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
• Rényi Mutual Information for Free Scalar in Even Dimensions
• On the Mutual Information in Conformal Field Theory
• Geometrizing the Partial Entanglement Entropy: from PEE Threads to Bit Threads
• Thermal Corrections to Renyi Entropies for Conformal Field Theories
• Bipartite Fluctuations and Topology of Dirac and Weyl Systems
• Multipartite entanglement and quantum Fisher information in conformal field theories
• Information flows in strongly coupled ABJM theory
• Negative tripartite mutual information after quantum quenches in integrable systems
• Universality in the tripartite information after global quenches
• Conformal bounds in three dimensions from entanglement entropy
• Entanglement entropy of inhomogeneous XX spin chains with algebraic interactions
• Aspects of N-partite information in conformal field theories
• Rényi entanglement entropies for the compactified massless boson with open boundary conditions
• Entanglement Structures in Quantum Field Theories II: Distortions of Vacuum Correlations Through the Lens of Local Observers
• Correspondence between Entanglement Growth and Probability Distribution of Quasi-Particles
• Quantum scrambling via accessible tripartite information
• Universality in the tripartite information after global quenches: (generalised) quantum XY models
• Loop Quantum Gravity and Quantum Information
• Probing trihedral corner entanglement for Dirac fermions
• Holographic Calculation of BMSFT Mutual and 3-partite Information
• Shape dependence of two-cylinder Renyi entropies for free bosons on a lattice
• Modular parallel transport of multiple intervals in 1+1-dimensional free fermion theory
• On universal terms of holographic entanglement entropy in theories with hyperscaling violation
• Subsystem entropy in 2d CFT and KdV ETH
• Entanglement structures from modified IR geometry
• An Operator Product Expansion for the Mutual Information in AdS/CFT
• Harvesting Fermionic Field Entanglement in Schwarzschild Spacetime
• Entanglement and entropy in multipartite systems: a useful approach
• Holographic n-partite Information in Hyperscaling Violating Geometry
• An operational definition of quantum information scrambling
• First Law and Quantum Correction for Holographic Entanglement Contour
• Entanglement Entropy with a Time-dependent Hamiltonian
• Entanglement Spectrum in General Free Fermionic Systems
• Mutual information from modular flow in CFTs
• Holographic Mutual Information of Two Disjoint Spheres
• Information paradox and island of covariant black holes in LQG
• More on entanglement properties of $Li{f}_4^{(2)}\times S^1\times S^5$ spacetime with string excitations
• Weaving the (AdS) spaces with partial entanglement entropy threads
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Shape dependence of mutual information in the OPE limit: linear responses
• Scrambling in Ising spin systems with periodic transverse magnetic fields
• Is the EMI model a QFT? An inquiry on the space of allowed entropy functions
• Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium
• Critical exponents of block-block mutual information in one-dimensional infinite lattice systems
• Causal shadow and non-local modular flow: from degeneracy to perturbative genesis by correlation
• Entropy of Hawking Radiation for Two-Sided Hyperscaling Violating Black Branes
• Disks globally maximize the entanglement entropy in $2+1$ dimensions
• Holographic Tensor Networks as Tessellations of Geometry
• New insights on mutual information in the island approach to the Page curve
• Evolution of the holographic entanglement entropy quantities for composite quantum systems