Hyperuniform charge distributions and phase transitions in a generalized Aubry-Andr\'e model (opens in new tab)

We show the existence of distinct inhomogeneous charge distributions and a phase transition between them in aperiodic fermion systems. Using a generalized Aubry-Andr\'e model as an example, we obtain various types of charge distributions, which we classify by means of hyperuniformity, a general mean to quantify and classify the global uniformity of spatial distributions. Examining various cases of filling fraction and potential strength and sh...