Entanglement entropy of two disjoint intervals in conformal field theory II

Abstract

We continue the study of the entanglement entropy of two disjoint intervals in conformal field theories that we started in J. Stat. Mech. (2009) P11001. We compute Trρ_A^n for any integer n for the Ising universality class and the final result is expressed as a sum of Riemann-Siegel theta functions. These predictions are checked against existing numerical data. We provide a systematic method that gives the full asymptotic expansion of the scaling function for small four-point ratio (i.e. short intervals). These formulas are compared with the direct expansion of the full results for free compactified boson and Ising model. We finally provide the analytic continuation of the first term in this expansion in a completely analytic form.

arXiv comment31 pages, 4 figures

References in corpus (38)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Aspects of Holographic Entanglement Entropy
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy and conformal field theory
• On Geometric Entropy
• Holographic Entanglement Entropy: An Overview
• Entanglement Renyi entropies in holographic theories
• Applied Conformal Field Theory
• A finite entanglement entropy and the c-theorem
• Entanglement spectrum in one-dimensional systems
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Quantum Noise as an Entanglement Meter
• Entanglement entropy of two disjoint intervals in conformal field theory
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• A holographic proof of the strong subadditivity of entanglement entropy
• Entanglement and alpha entropies for a massive Dirac field in two dimensions
• Remarks on the entanglement entropy for disconnected regions
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Entanglement entropy of two disjoint blocks in XY chains
• Reduced density matrix and internal dynamics for multicomponent regions
• Entanglement Entropy and Twist Fields
• Entanglement entropy of two disjoint blocks in critical Ising models
• Universal entanglement entropy in 2D conformal quantum critical points
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Critical and noncritical long range entanglement in the Klein-Gordon field
• Scaling of entanglement between separated blocks in spin chains at criticality
• Universality of the negativity in the Lipkin-Meshkov-Glick model
• On reduced density matrices for disjoint subsystems
• Holographic entanglement entropy for disconnected regions
• Entanglement, combinatorics and finite-size effects in spin-chains
• Entanglement of two blocks of spins in the critical Ising model
• Bethe Ansatz derived from the functional relations of the open XXZ chain for new special cases
• Thomae type formulae for singular Z_N curves
• Off-diagonal correlations in one-dimensional anyonic models: A replica approach
• Entropy inequalities from reflection positivity

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