Notes on Quantum Entanglement of Local Operators
arXiv:1405.5875 · doi:10.1007/JHEP10(2014)147
Abstract
This is an expanded version of the short report arXiv:1401.0539, where we stud- ied the (Renyi) entanglement entropies for the excited state defined by acting a given local operator on the ground state. We introduced the (Renyi) entanglement entropies of given local operators which measure the degrees of freedom of local operators and characterize them in conformal field theories from the viewpoint of quantum entanglement. In present paper, we explain how to compute them in free massless scalar field theories and we also investigate their time evolution. The results are interpreted in terms of relativistic propagation of an entangled pair. The main new results which we acquire in the present paper are as follows. Firstly, we provide an explanation which shows that the (Renyi) entanglement entropies of a specific operator are given by (Renyi) entanglement entropies of binomial distribution by the replica method. That operator is constructed of only scalar field. Secondly, we found the sum rule which (Renyi) entanglement entropies of those local operators obey. Those local operators are located separately. Moreover we argue that (Renyi) entanglement entropies of specific operators in conformal field theories are given by (Renyi) entanglement entropies of binomial distribution. These specific operators are constructed of single-species operator. We also argue that general operators obey the sum rule which we mentioned above.
arXiv comment44 pages, 14 figures, v2 references added
References in corpus (45)
- 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
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Time-dependence of correlation functions following a quantum quench
- Building up spacetime with quantum entanglement
- Time Evolution of Entanglement Entropy from Black Hole Interiors
- Gravitation from Entanglement in Holographic CFTs
- Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
- Gravitational Dynamics From Entanglement "Thermodynamics"
- Relative Entropy and Holography
- Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
- Thermodynamical Property of Entanglement Entropy for Excited States
- Entanglement Temperature and Entanglement Entropy of Excited States
- Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
- Holographic Local Quenches and Entanglement Density
- Entanglement of low-energy excitations in Conformal Field Theory
- Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
- Quantum Entanglement of Local Operators in Conformal Field Theories
- Evolution of entanglement after a local quench
- Exact results for the entanglement entropy and the energy radiated by a quark
- Entanglement Entropy in the O(N) model
- Weak Field Black Hole Formation in Asymptotically AdS Spacetimes
- Quantum quench in interacting field theory: a self-consistent approximation
- Holographic Superfluids and the Dynamics of Symmetry Breaking
- Universal entanglement entropy in 2D conformal quantum critical points
- Holographic Thermalization with Chemical Potential
- Observing complex bound states in the spin-1/2 Heisenberg XXZ chain using local quantum quenches
- Quantum quenches of holographic plasmas
- Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT
- Thermal quenches in N=2* plasmas
- Quantum Quench across a Holographic Critical Point
- Spin-charge separation in two-component Bose-gases
- Dynamical entanglement entropy with angular momentum and U(1) charge
- On generalized gravitational entropy, squashed cones and holography
- Entanglement entropy in higher derivative holography
- Quantum Quench Across a Zero Temperature Holographic Superfluid Transition
- Entropic Counterpart of Perturbative Einstein Equation
- Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining
- Holographic Geometry of cMERA for Quantum Quenches and Finite Temperature
- Dynamics of holographic thermalization
- Holographic Quantum Quench
- Note on Entanglement Temperature for Low Thermal Excited States in Higher Derivative Gravity
- Entanglement Entropy of Two Spheres
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- Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
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- Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench
- Scrambling time from local perturbations of the eternal BTZ black hole
- Higher-point conformal blocks and entanglement entropy in heavy states
- Holographic Quantum Circuits from Splitting/Joining Local Quenches
- Relative entropy of excited states in two dimensional conformal field theories
- Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
- Nonlocal probes of thermalization in holographic quenches with spectral methods
- Rényi entropy of locally excited states with thermal and boundary effect in 2D CFTs
- Charged Entanglement Entropy of Local Operators
- Entanglement constant for conformal families
- EPR Pairs, Local Projections and Quantum Teleportation in Holography
- Double Local Quenches in 2D CFTs and Gravitational Force
- Renyi Entropy for Local Quenches in 2D CFTs from Numerical Conformal Blocks
- Universal corrections to entanglement entropy of local quantum quenches
- Left-Right Entanglement Entropy of Boundary States
- Entanglement Wedges from Information Metric in Conformal Field Theories
- The quasi-particle picture and its breakdown after local quenches: mutual information, negativity, and reflected entropy
- Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs
- Entanglement and chaos in warped conformal field theories
- SVD Entanglement Entropy
- Entanglement and geometry from subalgebras of the Virasoro algebra
- Scattering effect on entanglement propagation in RCFTs
- Quantum Entanglement of Fermionic Local Operators
- Local quenches, bulk entanglement entropy and a unitary Page curve
- On the real-time evolution of pseudo-entropy in 2d CFTs
- Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
- Evolution of Entanglement Entropy in Orbifold CFTs
- Capacity of Entanglement in Local Operators
- Looking at Shadows of Entanglement Wedges
- Entanglement evolution across a conformal interface
- Holographic Entanglement Entropy For a Large Class of States in 2D CFT
- Quantum Entanglement of Locally Excited States in Maxwell Theory
- Out-of-Time-Ordered Correlators in
- Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2 + 1-dimensional Quantum Lifshitz Model
- Entanglement Entropy after Double-Excitation as Interaction Measure
- Entanglement Entropy of Disjoint Regions in Excited States : An Operator Method
- Pseudo Entropy in gauge theory
- Subsystem distance after a local operator quench
- Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory -- I. Single-particle states
- Multi-entropy at low Renyi index in 2d CFTs
- Quantum dimensions from local operator excitations in the Ising model
- On the Shape Dependence of Entanglement Entropy
- Pseudo entropy under joining local quenches
- Holographic Entanglement Entropy of Local Quenches in AdS/CFT: A Finite-Element Approach
- Entanglement spreading after local fermionic excitations in the XXZ chain
- Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians
- Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators
- Localized Excitations from Localized Unitary Operators
- Universal Local Operator Quenches and Entanglement Entropy
- Correspondence between Entanglement Growth and Probability Distribution of Quasi-Particles
- Subsystem complexity after a local quantum quench
- From locality to irregularity: Introducing local quenches in massive scalar field theory
- Correlation functions and quantum measures of descendant states
- A falling magnetic monopole as a holographic local quench
- Entanglement entropy of local gravitational quenches
- Time Evolution after Double Trace Deformation
- Entanglement Entropy and Conformal Collider Physics in 2D CFTs
- Entanglement spreading after local and extended excitations in a free-fermion chain
- Entanglement Suppression Due to Black Hole Scattering