Entanglement entropy and hyperuniformity of Ginibre and Weyl-Heisenberg ensembles

Abstract: We show that, for a class of planar determinantal point processes (DPP) X, the entanglement entropy of X on a compact region grows exactly at the rate of the variance fluctuation in that region. Therefore, such DPPs satisfy an area law if they are of Class I hyperuniformity, while the area law is violated if they are of Class II hyperuniformity. As a result, the entanglement entropy of Weyl-Heisenberg ensembles (a family of DPPs containing the Ginibre ensemble and Ginibre-type ensembles in higher Landau levels), satisfies an area law, as a consequence of its hyperuniformity.