Entanglement entropy and hyperuniformity of Ginibre and Weyl–Heisenberg ensembles

We show that, for a class of planar determinantal point processes (DPP) [Formula: see text] , the growth of the entanglement entropy [Formula: see text] of [Formula: see text] on a compact region [Formula: see text] , is related to the variance [Formula: see text] as follows: [Formula: see text] Therefore, such DPPs satisfy an area law [Formula: see text] , where [Formula: see text] is the boundary of [Formula: see text] if they are of Class I hyperuniformity ([Formula: see text] ), while the area law is violated if they are of Class II hyperuniformity (as [Formula: see text] , [Formula: see text] ). 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.