Entanglement entropy for non-coplanar regions in quantum field theory

Abstract

We study the entanglement entropy in a relativistic quantum field theory for regions which are not included in a single spatial hyperplane. This geometric configuration cannot be treated with the Euclidean time method and the replica trick. Instead, we use a real time method to calculate the entropy for a massive free Dirac field in two dimensions in some approximations. We find some specifically relativistic features of the entropy. First, there is a large enhancement of entanglement due to boosts. As a result, the mutual information between relatively boosted regions does not vanish in the limit of zero volume and large relative boost. We also find extensivity of the information in a deeply Lorentzian regime with large violations of the triangle inequalities for the distances. This last effect is relevant to an interpretation of the amount of entropy enclosed in the Hawking radiation emitted by a black hole.

20 pages, 7 figures

References in corpus (18)

• Towards a derivation of holographic entanglement entropy
• Area laws in quantum systems: mutual information and correlations
• Holographic c-theorems in arbitrary dimensions
• Entanglement Renyi entropies in holographic theories
• Entanglement as a Probe of Confinement
• Seeing a c-theorem with holography
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Remarks on the entanglement entropy for disconnected regions
• Holographic Entanglement Entropy in Lovelock Gravities
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Entanglement entropy of two disjoint blocks in XY chains
• Entanglement Entropy and Twist Fields
• Measurement of the Underlying Event Activity at the LHC with sqrt(s)= 7 TeV and Comparison with sqrt(s) = 0.9 TeV
• Some Calculable Contributions to Entanglement Entropy
• Entanglement entropy of two disjoint intervals in c=1 theories
• Holographic entanglement entropy: near horizon geometry and disconnected regions
• The Subleading Term of the Strong Coupling Expansion of the Heavy-Quark Potential in a $\mathcal{N}=4$ Super Yang-Mills Plasma
• The Physics of Information

Cited by in corpus (16)

• Finite temperature entanglement negativity in conformal field theory
• Entanglement negativity after a global quantum quench
• Entanglement negativity in the critical Ising chain
• Holographic Quantum Circuits from Splitting/Joining Local Quenches
• Entanglement negativity and conformal field theory: a Monte Carlo study
• Bound states and entanglement in the excited states of quantum spin chains
• Comments on Jacobson's "Entanglement equilibrium and the Einstein equation"
• Positivity, entanglement entropy, and minimal surfaces
• Evolution of Entanglement Entropy in Orbifold CFTs
• Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation
• Holographic Entanglement Entropy on Generic Time Slices
• Multipartite entanglement and quantum Fisher information in conformal field theories
• Universality in the tripartite information after global quenches: (generalised) quantum XY models
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium
• Quantum information measures and their applications in quantum field theory