Modular Nuclearity and Entanglement measures

Abstract: In the framework of Algebraic Quantum Field Theory, several operator algebraic notions of entanglement entropy can be associated to a couple of causally disjoint and distant spacetime regions $\mathcal{S}_A$ and $\mathcal{S}_B$. In this work, we show that the mutual information is finite in any local QFT verifying a modular $p$-nuclearity condition for some $0 < p <1$. A similar result is proved for another recently studied entanglement measure. Furthermore, if we assume conformal covariance then by comparison with other entanglement measures we can state that the mutual information satisfies lower bounds of area law type when the distance between $\mathcal{S}_A$ and $\mathcal{S}_B$ approaches to zero. As an application, in $1+1$-dimensional integrable models with factorizing S-matrices, we study the asymptotic behaviour of different entanglement measures as the distance between two causally disjoint wedges diverges.