Area Law from Loop Quantum Gravity

Abstract

We explore the constraints following from requiring the Area Law in the entanglement entropy in the context of loop quantum gravity. We find a unique solution to the single link wave-function in the large j limit, believed to be appropriate in the semi-classical limit. We then generalize our considerations to multi-link coherent states, and find that the area law is preserved very generically using our single link wave-function as a building block. Finally, we develop the framework that generates families of multi-link states that preserve the area law while avoiding macroscopic entanglement, the space-time analogue of "Schroedinger cat". We note that these states, defined on a given set of graphs, are the ground states of some local Hamiltonian that can be constructed explicitly. This can potentially shed light on the construction of the appropriate Hamiltonian constraints in the LQG framework.

6+5 pages, 2 figures, presentation improved, appendices added, revised version accepted for publication in Physical Review D

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• Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
• Typicality in spin network states of quantum geometry
• Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy
• Curvature from multipartite entanglement in quantum gravity states
• Semiclassical Length Measure from a Quantum-Gravity Wave Function