Hyperuniform electron distributions on the Ammann-Beenker tiling

We study the electron charge distribution on a quasiperiodic tiling in terms of hyperuniformity. In an extended Hubbard model on the Ammann-Beenker tiling, the electron distribution changes significantly with the Fermi energy and electron-interaction strength. Unlike periodic systems, these changes are not characterized by translational-symmetry breaking. We show that the electron charge distribution is not characterized by multifractality, either. We find that the distribution is instead characterized by hyperuniformity of Class I.