Modular Nuclearity and Entanglement Entropy

• URL: http://arxiv.org/abs/2108.09074v2
• Date: Wed, 8 Sep 2021 11:43:14 GMT
• Title: Modular Nuclearity and Entanglement Entropy
• Authors: Lorenzo Panebianco, Benedikt Wegener
• Abstract summary: In this work we show that the Longo's canonical entanglement entropy is finite in any local QFT verifying a modular $p$-nuclearity condition. As application, in $1+1$-dimensional integrable models with factorizing S-matrices we study the behavior of the canonical entanglement entropy as the distance between two causally disjoint wedges diverges.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the framework of Quantum Field Theory, several operator algebraic notions of entanglement entropy can be associated to any couple of causally disjoint and distant spacetime regions $\mathcal{S}_A$ and $\mathcal{S}_B$. In this work we show that the Longo's canonical entanglement entropy is finite in any local QFT verifying a modular $p$-nuclearity condition for some $0 < p <1$. Furthermore, if we assume conformal covariance then by comparison with other entanglement measures we can state that this entanglement entropy satisfies lower bounds of area law type when the distance between $\mathcal{S}_A$ and $\mathcal{S}_B$ approaches to zero. As application, in $1+1$-dimensional integrable models with factorizing S-matrices we study the asymptotic behavior of the canonical entanglement entropy as the distance between two causally disjoint wedges diverges.

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