Remarks on entanglement entropy for gauge fields
arXiv:1312.1183 · doi:10.1103/PhysRevD.89.085012
Abstract
In gauge theories the presence of constraints can obstruct expressing the global Hilbert space as a tensor product of the Hilbert spaces corresponding to degrees of freedom localized in complementary regions. In algebraic terms, this is due to the presence of a center --- a set of operators which commute with all others --- in the gauge invariant operator algebra corresponding to finite region. A unique entropy can be assigned to algebras with center, giving place to a local entropy in lattice gauge theories. However, ambiguities arise on the correspondence between algebras and regions. In particular, it is always possible to choose (in many different ways) local algebras with trivial center, and hence a genuine entanglement entropy, for any region. These choices are in correspondence with maximal trees of links on the boundary, which can be interpreted as partial gauge fixings. This interpretation entails a gauge fixing dependence of the entanglement entropy. In the continuum limit however, ambiguities in the entropy are given by terms local on the boundary of the region, in such a way relative entropy and mutual information are finite, universal, and gauge independent quantities.
26 pages, 7 figures
References in corpus (4)
Cited by in corpus (229)
- Bulk Locality and Quantum Error Correction in AdS/CFT
- Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
- Relative entropy equals bulk relative entropy
- Causality & holographic entanglement entropy
- The Ryu-Takayanagi Formula from Quantum Error Correction
- Quantum Simulation for High Energy Physics
- Entanglement entropy: holography and renormalization group
- Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture
- Entanglement entropy of electromagnetic edge modes
- Bulk locality from modular flow
- Inconsistency of Islands in Theories with Long-Range Gravity
- Exact results for the entanglement entropy and the energy radiated by a quark
- On The Entanglement Entropy For Gauge Theories
- Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
- U(1) Wilson lattice gauge theories in digital quantum simulators
- Entwinement and the emergence of spacetime
- Entanglement entropy and nonabelian gauge symmetry
- Geometric entropy and edge modes of the electromagnetic field
- Observables, gravitational dressing, and obstructions to locality and subsystems
- Aspects of Entanglement Entropy for Gauge Theories
- Flat entanglement spectra in fixed-area states of quantum gravity
- Entanglement Suppression and Emergent Symmetries of Strong Interactions
- Local phase space and edge modes for diffeomorphism-invariant theories
- Quantum Simulation and Spectroscopy of Entanglement Hamiltonians
- Holographic Renyi Entropy from Quantum Error Correction
- Tensor Networks for Lattice Gauge Theories with continuous groups
- Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
- Entanglement and symmetry resolution in two dimensional free quantum field theories
- Physics at the entangling surface
- Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
- Symmetry-resolved dynamical purification in synthetic quantum matter
- Universal Entanglement and Boundary Geometry in Conformal Field Theory
- Confinement and lack of thermalization after quenches in the bosonic Schwinger model
- A Holographic Derivation of the Weak Gravity Conjecture
- Quantum Information in Holographic Duality
- Nuts and Bolts for Creating Space
- Modular Hamiltonian of Excited States in Conformal Field Theory
- Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy
- Failure of the split property in gravity and the information paradox
- Symmetry resolved relative entropies and distances in conformal field theory
- Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
- Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem
- The entanglement of distillation for gauge theories
- Lorentz-diffeomorphism edge modes in 3d gravity
- Typical entanglement entropy in the presence of a center: Page curve and its variance
- Kitaev's quantum double model as an error correcting code
- Quantum Relativity of Subsystems
- Edge Dynamics from the Path Integral: Maxwell and Yang-Mills
- Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
- Entropic order parameters for the phases of QFT
- Entanglement entropy for a Maxwell field: Numerical calculation on a two dimensional lattice
- Living on the Edge: A Toy Model for Holographic Reconstruction of Algebras with Centers
- Thermalization of Gauge Theories from their Entanglement Spectrum
- Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space
- Edge modes as reference frames and boundary actions from post-selection
- A proposal for 3d quantum gravity and its bulk factorization
- Gauging the Kitaev chain
- Entwinement in discretely gauged theories
- Entanglement Entropy in (3+1)-d Free Gauge Theory
- Extended actions, dynamics of edge modes, and entanglement entropy
- Area terms in entanglement entropy
- Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory
- Renyi entropy, stationarity, and entanglement of the conformal scalar
- Entanglement entropy of a Maxwell field on the sphere
- Holographic entanglement entropy and the internal space
- Diffeomorphism invariance and the black hole information paradox
- Entanglement Entropy of U(1) Quantum Spin Liquids
- Systematically Localizable Operators for Quantum Simulations of Quantum Field Theories
- Three-dimensional de Sitter horizon thermodynamics
- Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
- Entanglement in Four-Dimensional SU(3) Gauge Theory
- The Hilbert Space of Quantum Gravity Is Locally Finite-Dimensional
- Entanglement guided search for parent Hamiltonians
- Gauging the Boundary in Field-space
- Gauge-invariant Variables and Entanglement Entropy
- Notes on Entanglement in Abelian Gauge Theories
- Entanglement Entropy in 2D Non-abelian Pure Gauge Theory
- Interacting systems and wormholes
- Bulk entanglement entropy in perturbative excited states
- A universal formula for the entanglement asymmetry of matrix product states
- Entanglement branes and factorization in conformal field theory
- Entanglement entropy production in gravitational collapse: covariant regularization and solvable models
- Comments on Entanglement Entropy in String Theory
- Comments on black hole interiors and modular inclusions
- Symmetry-Protected Topological Interfaces and Entanglement Sequences
- Quantum information measures for restricted sets of observables
- Deep Quantum Geometry of Matrices
- Internal quantum reference frames for finite Abelian groups
- Newton constant, contact terms and entropy
- Anomalies of the Entanglement Entropy in Chiral Theories
- Entanglement entropy of gravitational edge modes
- Electromagnetic Duality and Entanglement Anomalies
- Matrix Quantization of Gravitational Edge Modes
- Approximate Bacon-Shor Code and Holography
- Fermionization of conformal boundary states
- Entanglement entropy of Bell-network states in LQG: Analytical and numerical results
- Large Field Inflation and Gravitational Entropy
- Quantum Null Geometry and Gravity
- On the logarithmic coefficient of the entanglement entropy of a Maxwell field
- Entanglement versus entwinement in symmetric product orbifolds
- Entanglement branes, modular flow, and extended topological quantum field theory
- Origin of the quantum group symmetry in 3d quantum gravity
- Bulk entanglement entropy for photons and gravitons in AdS
- Entanglement entropy of linearized gravitons in a sphere
- Target space entanglement in Matrix Models
- A Survey of Black Hole Thermodynamics
- Entanglement Entropy of ()-Dimensional SU(2) Lattice Gauge Theory on Plaquette Chains
- Higher-curvature corrections to holographic entanglement entropy in geometries with hyperscaling violation
- Target Space Entanglement Entropy
- Area, Entanglement Entropy and Supertranslations at Null Infinity
- Canonical Transformations and Loop Formulation of SU(N) Lattice Gauge Theories
- Black Hole Horizon Edge Partition Functions
- Superselection Sectors of Gravitational Subregions
- Entanglement between two gravitating universes
- Black Hole and de Sitter Microstructures from a Semiclassical Perspective
- A Type Approximation of the Crossed Product
- Squeezed vacua in loop quantum gravity
- Symplectic reduction of Yang-Mills theory with boundaries: from superselection sectors to edge modes, and back
- Entanglement Properties of Gauge Theories from Higher-Form Symmetries
- Revisiting noninteracting string partition functions in Rindler space
- A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC
- Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
- Entanglement and RG in the vector model
- Entanglement in the Quantum Hall Matrix Model
- Entwinement as a possible alternative to complexity
- Gauge Structures: From Stabilizer Codes to Continuum Models
- A note on entanglement entropy and quantum geometry
- Towards a dual spin network basis for (3+1)d lattice gauge theories and topological phases
- Quantum exponentials for the modular double and applications in gravity models
- Statistical Mechanics of Monitored Dissipative Random Circuits
- Holographic Tensor Networks with Bulk Gauge Symmetries
- Perturbative unitarity bounds from momentum-space entanglement
- Area Law from Loop Quantum Gravity
- Strong Coupling Expansion of the Entanglement Entropy of Yang-Mills Gauge Theories
- Symmetry Resolution in non-Lorentzian Field Theories
- Momentum Space Entanglement from the Wilsonian Effective Action
- Universal Bounds on the Time Evolution of Entanglement Entropy
- Entanglement and confinement in lattice gauge theory tensor networks
- Entanglement entropy, dualities, and deconfinement in gauge theories
- Entropic order parameters in weakly coupled gauge theories
- Duality transformations and the entanglement entropy of gauge theories
- Quantum information probes of charge fractionalization in large- gauge theories
- Entanglement Entropy in Scalar Quantum Electrodynamics
- Randomized measurement protocols for lattice gauge theories
- Soft edges: the many links between soft and edge modes
- Partition functions of higher derivative conformal fields on conformally related spaces
- Target space entanglement in quantum mechanics of fermions and matrices
- Multipartite edge modes and tensor networks
- On entanglement entropy in 't Hooft model
- Quantum thermodynamics of nonequilibrium processes in lattice gauge theories
- Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories
- Quantum Information Theory of the Gravitational Anomaly
- Entanglement Entropy for 2D Gauge Theories with Matters
- Non-abelian symmetry-resolved entanglement entropy
- On the Entanglement Entropy of Quantum Fields in Causal Sets
- Entanglement Entropy in Jackiw-Teitelboim Gravity
- Interfaces and the extended Hilbert space of Chern-Simons theory
- Bosonic and fermionic Gaussian states from Kähler structures
- Disentangling (2+1)d Topological States of Matter with the Entanglement Negativity
- Instability of Universal Terms in the Entanglement Entropy
- Localized Excitations from Localized Unitary Operators
- Definitions of entwinement
- Numerical calculations on the relative entanglement entropy in critical spin chains
- Minimal Areas from Entangled Matrices
- Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization
- The quasilocal degrees of freedom of Yang-Mills theory
- 't Hooft suppression and holographic entropy
- Topological string entanglement
- Geometry of the Shannon mutual information in continuum QFT
- Quantum edge modes in 3d gravity and 2+1d topological phases of matter
- Twistor representation of Jackiw-Teitelboim gravity
- Dress code for infrared safe scattering in QED
- Emergent Area Laws from Entangled Matrices
- The Lattice-Continuum Correspondence in the Ising Model
- Electric-Magnetic Dualities in Non-Abelian and Non-Commutative Gauge Theories
- A Toy Model of Entwinement
- Quantum Mechanics in the Infrared
- Universal entanglement timescale for Rényi entropies
- Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
- Quantum group origins of edge states in double-scaled SYK
- Spectral properties of critical 1+1D Abelian-Higgs model
- Entangled spins and ghost-spins
- Analysis of the Entanglement with Centers
- Entanglement entropy in lattice theories with Abelian gauge groups
- From Lattice Gauge Theories to Hydrogen Atoms
- Entanglement Witnessing for Lattice Gauge Theories
- Numerical determination of the entanglement entropy for a Maxwell field in the cylinder
- Rényi Entropy for a CFT with a gauge field: WZW theory on a branched torus
- A note on electromagnetic edge modes
- Dilaton shifts, probability measures, and decomposition
- Defining entanglement without tensor factoring: a Euclidean hourglass prescription
- The Ultraviolet Structure of Quantum Field Theories. Part 3: Gauge Theories
- Gauge choices and Entanglement Entropy of two dimensional lattice gauge fields
- Entanglement entropy in Jackiw-Teitelboim gravity with matter
- Heterotic Strings and Quantum Entanglement
- Dynamical Edge Modes in Yang-Mills Theory
- Entanglement Entropy with a Time-dependent Hamiltonian
- Entanglement entropy of a Rarita-Schwinger field in a sphere
- Charge fluctuation entropy of Hawking radiation: a replica-free way to find large entropy
- Holographic Mutual Information of Two Disjoint Spheres
- Toolkit for Scalar Fields in Universes with finite-dimensional Hilbert Space
- The Ryu-Takayanagi Formula from Quantum Error Correction: An Algebraic Treatment of the Boundary CFT
- Strong subadditivity and holography
- Entanglement entropy of physical states in hypercuboidally truncated spin foam quantum gravity
- Entanglement Rényi entropies in celestial holography
- Shrinking of Operators in Quantum Error Correction and AdS/CFT
- Topological Rényi and Entanglement Entropy for a 2d q-deformed Yang-Mills theory and its Chern-Simons dual
- Target Space Entanglement in Quantum Mechanics of Fermions and Matrices
- Extractable entanglement from a Euclidean hourglass
- Partition functions of -forms from Harish-Chandra characters
- Shape dependence of mutual information in the OPE limit: linear responses
- Notes on a few quasilocal properties of Yang-Mills theory
- Violation of Unitarity in Gravitational Subregions
- Approximate recovery with locality and symmetry constraints
- Boundary Conditions for the Entanglement Cut in 2D Conformal Field Theories
- Entanglement and magic on the light-front
- Entanglement entropy in lattices with non-abelian gauge groups
- Entanglement Entropy across the Lattice-Continuum Correspondence
- Aspects of Entanglement Entropy in Algebraic Quantum Field Theory
- Effects of Non-Conformal Boundary on Entanglement Entropy
- Entanglement content of kink excitations
- Bulk quantum corrections to entwinement
- Entanglement in a Maxwell Theory coupled to a non-relativistic particle
- On Entanglement Entropy of Maxwell fields in 3+1 dimensions
- Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach
- Generalized symmetries and Noether's theorem in QFT
- Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes
- On the Renormalization of Entanglement Entropy
- Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter