title: Scaling of Rényi entanglement entropies of the free fermi-gas ground state: a rigorous proof.
abstract: In a remarkable paper [Phys. Rev. Lett. 96, 100503 (2006)], Gioev and Klich conjectured an explicit formula for the leading asymptotic growth of the spatially bipartite von Neumann entanglement entropy of noninteracting fermions in multidimensional Euclidean space at zero temperature. Based on recent progress by one of us (A. V. S.) in semiclassical functional calculus for pseudodifferential operators with discontinuous symbols, we provide here a complete proof of that formula and of its generalization to Rényi entropies of all orders α>0. The special case α=1/2 is also known under the name logarithmic negativity and often considered to be a particularly useful quantification of entanglement. These formulas exhibiting a "logarithmically enhanced area law" have been used already in many publications.
authors.affiliation: Institut für Theoretische Physik, Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany and Fakultät für Mathematik und Informatik, FernUniversität Hagen, Universitätsstraße 1, 58097 Hagen, Germany.
authors.forename: Hajo
authors.initials: H
authors.lastname: Leschke
authors.affiliation: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom.
authors.forename: Alexander V
authors.initials: AV
authors.lastname: Sobolev
authors.affiliation: Fakultät für Mathematik und Informatik, FernUniversität Hagen, Universitätsstraße 1, 58097 Hagen, Germany.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Spitzer