Universal Thermal Corrections to Entanglement Entropy for Conformal Field Theories on Spheres
arXiv:1407.1358 · doi:10.1007/JHEP10(2014)028
Abstract
We consider entanglement entropy of a cap-like region for a conformal field theory living on a sphere times a circle in d space-time dimensions. Assuming that the finite size of the system introduces a unique ground state with a nonzero mass gap, we calculate the leading correction to the entanglement entropy in a low temperature expansion. The correction has a universal form for any conformal field theory that depends only on the size of the mass gap, its degeneracy, and the angular size of the cap. We confirm our result by calculating the entanglement entropy of a conformally coupled scalar numerically. We argue that an apparent discrepancy for the scalar can be explained away through a careful treatment of boundary terms. In an appendix, to confirm the accuracy of the numerics, we study the mutual information of two cap-like regions at zero temperature.
arXiv comment18 pages, 5 figures; v2, major revision, discrepancy explained (published version); v3, beta typo fixed, refs added
References in corpus (21)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Entanglement in quantum critical phenomena
- Entropy and Area
- Entanglement in a simple quantum phase transition
- Towards a derivation of holographic entanglement entropy
- Quantum corrections to holographic entanglement entropy
- Reduced density matrices and entanglement entropy in free lattice models
- Implications of Conformal Invariance in Field Theories for General Dimensions
- On the RG running of the entanglement entropy of a circle
- Relative Entropy and Holography
- Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
- Holographic entanglement beyond classical gravity
- Some Results on Mutual Information of Disjoint Regions in Higher Dimensions
- Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
- Entanglement Entropy of a Massive Fermion on a Torus
- Non-minimal coupling, boundary terms and renormalization of the Einstein-Hilbert action
- Single Interval Rényi Entropy At Low Temperature
- Renyi entropies of free bosons on the torus and holography
- Renyi entropy, stationarity, and entanglement of the conformal scalar
- Entanglement Entropy of Two Spheres
- Tracing Through Scalar Entanglement
Cited by in corpus (39)
- Entanglement entropy: holography and renormalization group
- Finite temperature entanglement negativity in conformal field theory
- Modular Hamiltonians on the null plane and the Markov property of the vacuum state
- Entanglement and symmetry resolution in two dimensional free quantum field theories
- Holographic Proof of the Quantum Null Energy Condition
- Some Aspects of Entanglement Wedge Cross-Section
- Entanglement Entropy for Relevant and Geometric Perturbations
- Relative entropy and the RG flow
- Quantum Corrections to Holographic Mutual Information
- Rényi entropy of locally excited states with thermal and boundary effect in 2D CFTs
- Holographic de Sitter Geometry from Entanglement in Conformal Field Theory
- Area terms in entanglement entropy
- Entanglement entropy of a Maxwell field on the sphere
- Monodromy Defects in Free Field Theories
- Renormalization group flow of entanglement entropy on spheres
- On the continuum limit of the entanglement Hamiltonian of a sphere for the free massless scalar field
- Entanglement Entropy of Disjoint Regions in Excited States : An Operator Method
- Entanglement Entropy of Annulus in Three Dimensions
- State-Dependent Divergences in the Entanglement Entropy
- Mutual information superadditivity and unitarity bounds
- On the Shape Dependence of Entanglement Entropy
- On the Mutual Information in Conformal Field Theory
- Rényi Mutual Information for Free Scalar in Even Dimensions
- Entanglement and RG in the vector model
- Entanglement entropy and differential entropy for massive flavors
- Mutual Rényi information for two disjoint compound systems
- Thermal Corrections to Renyi Entropies for Conformal Field Theories
- Mutual information on the fuzzy sphere
- Large- phase transitions in holographic mutual information
- The Edge of Entanglement: Getting the Boundary Right for Non-Minimally Coupled Scalar Fields
- Sakharov's induced gravity on the AdS background: SM scale as inverse mass parameter of the Schwinger-DeWitt expansion
- An Inverse Mass Expansion for the Mutual Information in Free Scalar QFT at Finite Temperature
- Renormalized Entanglement Entropy on Cylinder
- Thermal Corrections to Rényi Entropy in BMS Field Theory
- Thermal Corrections to Entanglement Entropy from Holography
- Thermal Correction to Entanglement Spectrum for Conformal Field Theories
- Thermal Corrections to Rényi entropies for Free Fermions
- Holographic Mutual Information at small separations
- Bekenstein bound in the bulk and AdS/CFT