The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes

Abstract

We study the area and volume laws for entanglement of free quantum scalar fields. In addition to the entropy, we use the notion of the capacity of entanglement, which measures entropy fluctuations. We consider flat spacetimes as well as the curved ones relevant for cosmology. Moreover, we put special emphasis on quench phenomena and different geometries of the entangling surfaces. First, we show that, in the Minkowski spacetime, the capacity of entanglement, like entropy, exhibits the area law for two kinds of geometries of the entangling surfaces: the sphere and strip. Moreover, we show that the ratio of both quantities takes the same values for both surfaces. Next, we turn our attention to quenches. Namely, we analyse the dynamics of capacity; in particular, contribution of the volume and surface terms. Moreover, we compare these results with theoretical predictions resulting from the quasiparticles model. In the second part, we consider the above issues for the FLRW spaces; especially, for de Sitter space as well as a metric modeling the transition to radiation-dominated era. Finally, we analyse the abrupt quenches in de Sitter space.

26 pages, 16 figures, additional comments and references, published version

References in corpus (31)

• Towards a derivation of holographic entanglement entropy
• Phase transitions in the early and the present Universe
• Entanglement negativity after a global quantum quench
• Some Calculable Contributions to Entanglement Entropy
• Probing Hawking radiation through capacity of entanglement
• Entanglement entropy of $\alpha$-vacua in de Sitter space
• Replica wormholes and capacity of entanglement
• Modular Fluctuations from Shockwave Geometries
• Real-space entanglement in the Cosmic Microwave Background
• Eigenstate capacity and Page curve in fermionic Gaussian states
• Capacity of Entanglement for Non-local Hamiltonian
• Real-space entanglement of quantum fields
• Subsystem complexity after a global quantum quench
• Capacity of Entanglement in Local Operators
• Capacity of entanglement in random pure state
• Entanglement of Harmonic Systems in Squeezed States
• Entanglement and Expansion
• Real-space quantum-to-classical transition of time dependent background fluctuations
• Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement
• Role of spatial higher order derivatives in momentum space entanglement
• Wavefunctions in dS/CFT revisited: principal series and double-trace deformations
• Horizon entanglement area law from regular black hole thermodynamics
• Average capacity of quantum entanglement
• Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields
• Entanglement in Cosmology
• Entanglement area law violation from field-curvature coupling
• Quantum quenches during inflation
• Aspects of dS/CFT Holography
• Quantum Area Fluctuations from Gravitational Phase Space
• Evolution of capacity of entanglement and modular entropy in harmonic chains and scalar fields
• Modular Fluctuations in Cosmology