Defining entanglement without tensor factoring: a Euclidean hourglass prescription

We consider entanglement across a planar boundary in flat space. Entanglement entropy is usually thought of as the von Neumann entropy of a reduced density matrix, but it can also be thought of as half the von Neumann entropy of a product of reduced density matrices on the left and right. The latter...

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Bibliographic Details
Published in:arXiv.org 2022-03
Main Authors: Anegawa, Takanori, Iizuka, Norihiro, Kabat, Daniel
Format: Article
Language:English
Subjects:
Cones
Density
Entanglement
Entropy
Euclidean geometry
Hilbert space
Mathematical analysis
Scalars
Tensors
Online Access:Get full text
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Summary:We consider entanglement across a planar boundary in flat space. Entanglement entropy is usually thought of as the von Neumann entropy of a reduced density matrix, but it can also be thought of as half the von Neumann entropy of a product of reduced density matrices on the left and right. The latter form allows a natural regulator in which two cones are smoothed into a Euclidean hourglass geometry. Since there is no need to tensor-factor the Hilbert space, the regulated entropy is manifestly gauge-invariant and has a manifest state-counting interpretation. We explore this prescription for scalar fields, where the entropy is insensitive to a non-minimal coupling, and for Maxwell fields, which have the same entropy as \(d-2\) scalars.
ISSN:2331-8422
DOI:10.48550/arxiv.2111.03886