Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks

Abstract

We reconsider the computation of the entanglement entropy of two disjoint intervals in a (1+1) dimensional conformal field theory by conformal block expansion of the 4-point correlation function of twist fields. We show that accurate results may be obtained by taking into account several terms in the operator product expansion (OPE) of twist fields and by iterating the Zamolodchikov recursion formula for each conformal block. We perform a detailed analysis for the Ising conformal field theory and for the free compactified boson. Each term in the conformal block expansion can be easily analytically continued and so this approach also provides a good approximation for the von Neumann entropy.

25 pages, 4 figures. New version: small changes in the main text, Fig.3 has been modified

References in corpus (19)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement negativity in quantum field theory
• Entanglement spectrum in one-dimensional systems
• Remarks on the entanglement entropy for disconnected regions
• Entanglement of low-energy excitations in Conformal Field Theory
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Maximally multipartite entangled states
• Entanglement entropy of two disjoint blocks in XY chains
• Entanglement Entropy and Twist Fields
• Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
• Entanglement spectrum of random-singlet quantum critical points
• Holographic entanglement entropy for disconnected regions
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Twist operators in higher dimensions
• Holographic entanglement entropy: near horizon geometry and disconnected regions
• Bose-Fermi duality and entanglement entropies
• On shape dependence of holographic mutual information in AdS4
• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Entanglement of several blocks in fermionic chains

Cited by in corpus (47)

• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Symmetry resolved entanglement entropy of excited states in a CFT
• Symmetry resolved relative entropies and distances in conformal field theory
• Symmetry resolved entanglement in integrable field theories via form factor bootstrap
• Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity
• U(1) symmetry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap
• Branch Point Twist Field Form Factors in the sine-Gordon Model II: Composite Twist Fields and Symmetry Resolved Entanglement
• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• Subsystem Trace Distance in Quantum Field Theory
• Entanglement as geometry and flow
• Charged Rényi negativity of massless free bosons
• Entanglement entropies of inhomogeneous Luttinger liquids
• Subsystem trace distance in low-lying states of $(1+1)$-dimensional conformal field theories
• Formulas for Partial Entanglement Entropy
• Multi-charged moments of two intervals in conformal field theory
• Holographic entanglement negativity for disjoint intervals in $Ad{S}_3/CF{T}_2$
• Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
• Entanglement Spheres and a UV-IR connection in Effective Field Theories
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory II: Numerics, Interacting Theories and Higher Dimensions
• Universality in asymptotic bounds and its saturation in $2$D CFT
• Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains
• Universal Rényi Entropy of Quasiparticle Excitations
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory -- I. Single-particle states
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states
• Universal entanglement and correlation measure in two-dimensional conformal field theories
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
• Rényi entanglement entropies for the compactified massless boson with open boundary conditions
• Wilsonian Effective Action and Entanglement Entropy
• Entanglement entropy in scalar field theory and ${\mathbb{Z}}_M$ gauge theory on Feynman diagrams
• Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators
• More on symmetry resolved operator entanglement
• Entanglement Structures in Quantum Field Theories II: Distortions of Vacuum Correlations Through the Lens of Local Observers
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
• Aspects of the S transformation Bootstrap
• Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• The operator algebra of cyclic orbifolds
• Scaling of finite size effect of $\alpha$-Rényi entropy in disjointed intervals under dilation
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Perturbative distinguishability of black hole microstates from AdS/CFT correspondence
• Measurement-Induced Entanglement in Conformal Field Theory
• Critical exponents of block-block mutual information in one-dimensional infinite lattice systems
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions
• Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium
• Subsystem fidelity in two-dimensional conformal field theories