A refinement of entanglement entropy and the number of degrees of freedom

Abstract

We introduce a "renormalized entanglement entropy" which is intrinsically UV finite and is most sensitive to the degrees of freedom at the scale of the size R of the entangled region. We illustrated the power of this construction by showing that the qualitative behavior of the entanglement entropy for a non-Fermi liquid can be obtained by simple dimensional analysis. We argue that the functional dependence of the "renormalized entanglement entropy" on R can be interpreted as describing the renormalization group flow of the entanglement entropy with distance scale. The corresponding quantity for a spherical region in the vacuum, has some particularly interesting properties. For a conformal field theory, it reduces to the previously proposed central charge in all dimensions, and for a general quantum field theory, it interpolates between the central charges of the UV and IR fixed points as R is varied from zero to infinity. We conjecture that in three (spacetime) dimensions, it is always non-negative and monotonic, and provides a measure of the number of degrees of freedom of a system at scale R. In four dimensions, however, we find examples in which it is neither monotonic nor non-negative.

54 pages, v2: Discussion of Renyi entropies and citations added, typos corrected

References in corpus (34)

• Towards a derivation of holographic entanglement entropy
• On Renormalization Group Flows in Four Dimensions
• Holographic c-theorems in arbitrary dimensions
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement as a Probe of Confinement
• On the RG running of the entanglement entropy of a circle
• Seeing a c-theorem with holography
• Hidden Fermi surfaces in compressible states of gauge-gravity duality
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Entanglement entropy, conformal invariance and extrinsic geometry
• The Constraints of Conformal Symmetry on RG Flows
• On Holographic Entanglement Entropy and Higher Curvature Gravity
• Holographic Fermi Surfaces and Entanglement Entropy
• Remarks on the entanglement entropy for disconnected regions
• Comments on Holographic Entanglement Entropy and RG Flows
• Entanglement Entropy, Trace Anomalies and Holography
• Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
• Entanglement entropy of critical spin liquids
• Some Calculable Contributions to Entanglement Entropy
• Bianchi Attractors: A Classification of Extremal Black Brane Geometries
• Holographic Entanglement Entropy and Fermi Surfaces
• Universal crossovers between entanglement entropy and thermal entropy
• Entanglement entropies in free fermion gases for arbitrary dimension
• Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors
• Numerical determination of the entanglement entropy for free fields in the cylinder
• Mutual information and the structure of entanglement in quantum field theory
• Holographic Entanglement Entropy and Renormalization Group Flow
• Holographic Entanglement Entropy at Finite Temperature
• c-theorem of the entanglement entropy
• Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?
• On higher derivative gravity, c-theorems and cosmology
• Higher Derivative Corrections to Holographic Entanglement Entropy for AdS Solitons
• Entanglement entropy for odd spheres
• Holographic Entanglement Entropy for d=4 N=2 SCFTs in F-theory

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• Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
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• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Comments on Holographic Entanglement Entropy and RG Flows
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• Holographic entanglement plateaux
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• Scaling Theory of Entanglement at the Many-Body Localization Transition
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• Dynamical entanglement entropy with angular momentum and U(1) charge
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• Probing renormalization group flows using entanglement entropy
• On Holographic Defect Entropy
• Bulk Emergence and the RG Flow of Entanglement Entropy
• Conformal Blocks and Negativity at Large Central Charge
• Entanglement entropy across a deformed sphere
• Corner contributions to holographic entanglement entropy
• Entanglement Entropy for Singular Surfaces
• Shape Dependence of Entanglement Entropy in Conformal Field Theories
• Holographic Entanglement Entropy in P-wave Superconductor Phase Transition
• Entanglement Entropy for Relevant and Geometric Perturbations
• Entanglement Entropy for $TT$ deformed CFT in general dimensions
• Relative entropy and the RG flow
• Observations on entanglement entropy in massive QFT's
• On entanglement spreading from holography
• Generalized $F$-Theorem and the $\epsilon$ Expansion
• Surface Counterterms and Regularized Holographic Complexity
• Exact and Numerical Results on Entanglement Entropy in (5+1)-Dimensional CFT
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• Nonlocal probes of thermalization in holographic quenches with spectral methods
• Corner contributions to holographic entanglement entropy in AdS4/BCFT3
• Disk entanglement entropy for a Maxwell field
• Irreversibility in quantum field theories with boundaries
• Entanglement entropy for a Maxwell field: Numerical calculation on a two dimensional lattice
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• Massive Anti-de Sitter Gravity from String Theory
• Renyi entropy, stationarity, and entanglement of the conformal scalar
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• Is entanglement a probe of confinement?
• Holographic Entanglement Negativity for Adjacent Subsystems in $\mathrm{Ad}{\mathrm{S}}_{\mathrm{d}+1}/CF{\mathrm{T}}_{\mathrm{d}}$
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• Holographic RG-flows and Boundary CFTs
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• Holographic RG flows on curved manifolds and the $F$-theorem
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• Topological Multipartite Entanglement in a Fermi Liquid
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• Entanglement Entropy of Extremal BTZ
• Lattice study of Rényi entanglement entropy in $SU(N_c)$ lattice Yang-Mills theory with $N_c=2,3,4$
• Two-cylinder entanglement entropy under a twist
• Non-local observables at finite temperature in AdS/CFT
• On shape dependence of holographic entanglement entropy in AdS4/CFT3
• Renormalization group flow of entanglement entropy on spheres
• Very General Holographic Superconductors and Entanglement Thermodynamics
• Two-component quantum Hall effects in topological flat bands
• Generalizing the entanglement entropy of singular regions in conformal field theories
• Entanglement entropy from non-equilibrium Monte Carlo simulations
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• Boomerang RG flows with intermediate conformal invariance
• On the continuum limit of the entanglement Hamiltonian of a sphere for the free massless scalar field
• On the logarithmic coefficient of the entanglement entropy of a Maxwell field
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• Renormalized Entanglement Entropy Flow in Mass-deformed ABJM Theory
• On c-theorems in arbitrary dimensions
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• Duality transformations and the entanglement entropy of gauge theories
• QNEC2 in deformed holographic CFTs
• 3d defects in 5d: RG flows and defect F-maximization
• Quantum information probes of charge fractionalization in large-$N$ gauge theories
• Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators
• On shape dependence of holographic entanglement entropy in AdS4/CFT3 with Lifshitz scaling and hyperscaling violation
• Entanglement entropy in scalar field theory and ${\mathbb{Z}}_M$ gauge theory on Feynman diagrams
• Comments on universal properties of entanglement entropy and bulk reconstruction
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