Entanglement Entropy and Spatial Geometry
Micheal S. Berger, Roman V. Buniy
TL;DR
This paper proves that for a free scalar field in any spatially curved geometry, the entanglement entropy between two regions is proportional to the hypersurface volume, providing a detailed asymptotic expansion.
Contribution
It establishes a general proof of the volume proportionality of entanglement entropy in arbitrary spatial geometries and derives a complete asymptotic expansion.
Findings
Entanglement entropy is proportional to hypersurface volume in arbitrary geometries.
Derived a complete asymptotic expansion for the entropy.
Confirmed the proportionality in complex spatial curvature scenarios.
Abstract
The entanglement entropy in a quantum field theory between two regions of space has been shown in simple cases to be proportional to the volume of the hypersurface separating the regions. We prove that this is true for a free scalar field in an arbitrary geometry with purely spatial curvature and obtain a complete asymptotic expansion for the entropy.
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