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.

References in corpus (4)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• Spectral deviation of concentration operators for the short-time Fourier transform
• Local number variances and hyperuniformity of the Heisenberg family of determinantal point processes

Cited by in corpus (3)

• Hyperuniformity of Maximally Random Jammed Packings of Hyperspheres Across Spatial Dimensions
• Theoretical Basis for Classifying Hyperuniform States of Two-Component Systems
• On accumulated spectrograms for Gabor frames