Shape Dependence of Entanglement Entropy in Conformal Field Theories

Abstract

We study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on ${\mathbb{R}}^{1,d-1}$. We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, and proportional to the coefficient $C_T$ appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient $\frac{\sigma }{C_T}=\frac{{\pi }^2}{24}$ in $d=3$ CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.

43 pages, 5 figures; v2: Typos fixed, additional references

References in corpus (11)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Towards a derivation of holographic entanglement entropy
• Holography from Conformal Field Theory
• Entanglement entropy, conformal invariance and extrinsic geometry
• Universality of corner entanglement in conformal field theories
• Bulk Emergence and the RG Flow of Entanglement Entropy
• Entanglement Entropy: A Perturbative Calculation
• On Shape Dependence and RG Flow of Entanglement Entropy
• Universality in the geometric dependence of Renyi entropy
• Entanglement Entropy for Relevant and Geometric Perturbations
• Bounds on corner entanglement in quantum critical states

Cited by in corpus (49)

• Quantum entanglement in condensed matter systems
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• Modular Hamiltonians on the null plane and the Markov property of the vacuum state
• A General Proof of the Quantum Null Energy Condition
• Rényi entropy and conformal defects
• Holographic Proof of the Quantum Null Energy Condition
• Quantum Corrections to Holographic Mutual Information
• Shape Dependence of Holographic Rényi Entropy in General Dimensions
• Superconformal surfaces in four dimensions
• Universal Features of Higher-Form Symmetries at Phase Transitions
• Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs
• Universality of squashed-sphere partition functions
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Scaling of disorder operator at $(2+1)d$ U(1) quantum criticality
• Energy is Entanglement
• Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice
• Multipartitioning topological phases by vertex states and quantum entanglement
• Two-cylinder entanglement entropy under a twist
• Local measures of entanglement in black holes and CFTs
• Higher Curvature Gravity from Entanglement in Conformal Field Theories
• Extracting subleading corrections in entanglement entropy at quantum phase transitions
• Entanglement entropy from one-point functions in holographic states
• Relating bulk to boundary entanglement
• A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow
• Incremental SWAP Operator for Entanglement Entropy: Application for Exponential Observables in Quantum Monte Carlo Simulation
• Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2 + 1-dimensional Quantum Lifshitz Model
• Universal signatures of Dirac fermions in entanglement and charge fluctuations
• Cornering gapless quantum states via their torus entanglement
• A universal feature of charged entanglement entropy
• Gravitational dual of the Rényi twist displacement operator
• Entanglement of skeletal regions
• Shape dependence of renormalized holographic entanglement entropy
• Dynamics of the Area Law of Entanglement Entropy
• Bipartite Fluctuations and Topology of Dirac and Weyl Systems
• Conformal bounds in three dimensions from entanglement entropy
• Geometric entanglement in integer quantum Hall states
• Entanglement susceptibilities and universal geometric entanglement entropy
• Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators
• Intertwining Operator in Thermal CFT${}_d$
• Bosonic and fermionic Gaussian states from Kähler structures
• An analog of topological entanglement entropy for mixed states
• Shape dependence of two-cylinder Renyi entropies for free bosons on a lattice
• Extracting Universal Corner Entanglement Entropy during the Quantum Monte Carlo Simulation
• The entanglement entropy of the quantum Hall edge and its geometric contribution
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Quantum information and the C-theorem in de Sitter
• Universal term of Entanglement Entropy in the $\pi$-flux Hubbard model
• Universal divergence of the Renyi entropy of a thinly sliced torus at the Ising fixed point
• Holography and the Page curve of an evaporating black hole