Modular Nuclearity and Entanglement Entropy

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.