Entanglement entropy, planar surfaces, and spectral functions

Abstract

We consider the universal part of entanglement entropy across a plane in flat space for a QFT, giving a non-perturbative expression in terms of a spectral function. We study the change in entanglement entropy under a deformation by a relevant operator, providing a pertrubative expansion where the terms are correlation functions in the undeformed theory. The entanglement entropy for free massive fermions and scalars easily follows. Finally, we study entanglement entropy across a plane in a background geometry that is a deformation of flat space, finding new universal terms arising from mixing of geometry and couplings of the QFT.

23 pages, 1 figure

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Cited by in corpus (32)

• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Bulk Emergence and the RG Flow of Entanglement Entropy
• Entanglement Entropy: A Perturbative Calculation
• Universality in the geometric dependence of Renyi entropy
• Aspects of capacity of entanglement
• Entanglement Entropy for Relevant and Geometric Perturbations
• Relative entropy and the RG flow
• Universal corner entanglement from twist operators
• Irreversibility in quantum field theories with boundaries
• Area terms in entanglement entropy
• Renormalization group flow of entanglement entropy on spheres
• Holographic entanglement entropy in the nonconformal medium
• Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation
• Entanglement Entropy of Annulus in Three Dimensions
• State-Dependent Divergences in the Entanglement Entropy
• Logarithmic Corrections to the Entanglement Entropy
• A Renyi Quantum Null Energy Condition: Proof for Free Field Theories
• Entanglement entropy and differential entropy for massive flavors
• Entanglement and RG in the $O(N)$ vector model
• Dynamics of the Area Law of Entanglement Entropy
• On the Shape Dependence of Entanglement Entropy
• Holographic RG flows, entanglement entropy and the sum rule
• Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators
• Wilsonian Effective Action and Entanglement Entropy
• Entanglement entropy in scalar field theory and ${\mathbb{Z}}_M$ gauge theory on Feynman diagrams
• The Edge of Entanglement: Getting the Boundary Right for Non-Minimally Coupled Scalar Fields
• The holographic dual of Rényi relative entropy
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• Non-Conformal Behavior of Holographic Entanglement Measures
• Composite operators in $T\bar{T}$-deformed free QFTs
• Quantum information and the C-theorem in de Sitter
• Universal terms of the entanglement entropy in a static closed universe