Entanglement Entropy for Relevant and Geometric Perturbations

Abstract

We continue the study of entanglement entropy for a QFT through a perturbative expansion of the path integral definition of the reduced density matrix. The universal entanglement entropy for a CFT perturbed by a relevant operator is calculated to second order in the coupling. We also explore the geometric dependence of entanglement entropy for a deformed planar entangling surface, finding surprises at second order.

arXiv comment18 pages + appendices

References in corpus (43)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Topological entanglement entropy
• Aspects of Holographic Entanglement Entropy
• Entropy and Area
• Towards a derivation of holographic entanglement entropy
• AdS/CFT Correspondence and Symmetry Breaking
• Generalized gravitational entropy
• On Geometric Entropy
• On Renormalization Group Flows in Four Dimensions
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Holographic c-theorems in arbitrary dimensions
• Entanglement entropy of black holes
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• Gravitation from Entanglement in Holographic CFTs
• Relative Entropy and Holography
• Entanglement entropy of random quantum critical points in one dimension
• Holographic Entanglement Entropy for General Higher Derivative Gravity
• Entanglement entropy, conformal invariance and extrinsic geometry
• Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions
• Implications of conformal invariance in momentum space
• Thermodynamical Property of Entanglement Entropy for Excited States
• A refinement of entanglement entropy and the number of degrees of freedom
• Entanglement Temperature and Entanglement Entropy of Excited States
• Generalized entropy and higher derivative Gravity
• On Holographic Entanglement Entropy and Higher Curvature Gravity
• F-Theorem without Supersymmetry
• Renormalization of Black Hole Entropy and of the Gravitational Coupling Constant
• Entanglement Entropy in the O(N) model
• Entanglement entropy and nonabelian gauge symmetry
• A non-renormalization theorem for conformal anomalies
• Some Calculable Contributions to Entanglement Entropy
• Some Calculable Contributions to Holographic Entanglement Entropy
• Entanglement Entropy: A Perturbative Calculation
• On Shape Dependence and RG Flow of Entanglement Entropy
• Universality in the geometric dependence of Renyi entropy
• Observations on entanglement entropy in massive QFT's
• Numerical determination of the entanglement entropy for free fields in the cylinder
• Universal Thermal Corrections to Entanglement Entropy for Conformal Field Theories on Spheres
• Entanglement entropy, planar surfaces, and spectral functions
• Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?
• Entanglement Entropy Flow and the Ward Identity
• A Comment on the Geometric Entropy and Conical Space
• Conformal a-charge, correlation functions and conical defects

Cited by in corpus (61)

• Entanglement entropy: holography and renormalization group
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• Universality of corner entanglement in conformal field theories
• Holographic Proof of the Quantum Null Energy Condition
• Bulk Emergence and the RG Flow of Entanglement Entropy
• Corner contributions to holographic entanglement entropy
• Aspects of capacity of entanglement
• Shape Dependence of Entanglement Entropy in Conformal Field Theories
• Universal corner entanglement from twist operators
• Relative entropy and the RG flow
• Irreversibility in quantum field theories with boundaries
• Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories
• Area terms in entanglement entropy
• The Holographic Shape of Entanglement and Einstein's Equations
• Comments on Squashed-sphere Partition Functions
• Local measures of entanglement in black holes and CFTs
• Renormalization group flow of entanglement entropy on spheres
• Towards Spacetime Entanglement Entropy for Interacting Theories
• Holographic entanglement entropy in the nonconformal medium
• Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation
• Thermodynamic law from the entanglement entropy bound
• Gravity duals of boundary cones
• Entanglement Entropy & Anomaly Inflow
• Logarithmic Corrections to the Entanglement Entropy
• State-Dependent Divergences in the Entanglement Entropy
• An Inverse Mass Expansion for Entanglement Entropy in Free Massive Scalar Field Theory
• A Renyi Quantum Null Energy Condition: Proof for Free Field Theories
• Entanglement entropy and differential entropy for massive flavors
• Entanglement Entropy for $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed holographic CFT
• Entanglement and RG in the $O(N)$ vector model
• On the Shape Dependence of Entanglement Entropy
• Dynamics of the Area Law of Entanglement Entropy
• Holographic RG flows, entanglement entropy and the sum rule
• Comments on universal properties of entanglement entropy and bulk reconstruction
• The first law of differential entropy and holographic complexity
• Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators
• Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories
• On entanglement entropy in 't Hooft model
• Wilsonian Effective Action and Entanglement Entropy
• Entanglement entropy in scalar field theory and ${\mathbb{Z}}_M$ gauge theory on Feynman diagrams
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• The holographic dual of Rényi relative entropy
• Non-conformal entanglement entropy
• Entanglement entropy of singular surfaces under relevant deformations in holography
• Composite operators in $T\bar{T}$-deformed free QFTs
• Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory
• Non-Conformal Behavior of Holographic Entanglement Measures
• Endpoint contributions to excited-state modular Hamiltonians
• Sine-Gordon Theory : Entanglement entropy and holography
• Holographic Entanglement Entropy for Gravitational Anomaly in Four Dimensions
• Entanglement Entropy with a Time-dependent Hamiltonian
• Time Evolution after Double Trace Deformation
• Localized thermal states and negative energy
• Holographic entanglement entropy probe on spontaneous symmetry breaking with vector order
• Shape dependence of mutual information in the OPE limit: linear responses
• Generalised proofs of the first law of entanglement entropy
• Universal thermalization dynamics in (1+1)d QFTs
• Entanglement entropy and complexity of singular subregions in deformed CFT
• The Area Term of the Entanglement Entropy of a Supersymmetric $O(N)$ Vector Model in Three Dimensions
• Causal shadow and non-local modular flow: from degeneracy to perturbative genesis by correlation
• Holography and the Page curve of an evaporating black hole