Statistical Interaction Description of Pauli Crystals in 2D Systems of Harmonically Confined Fermions

It is conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures, called Pauli crystals, are predicted for a two-dimensional (2D) system of free fermions under harmonic confinement. In this work, the possibility of this outcome is pursued and a theoretical model is considered that may capture both qualitatively and quantitatively, the key features of the abovementioned setup. The results for N=3 and 6 particles show that the minimum energy configuration corresponds to and is in good quantitative agreement with the reported values of Pauli crystals seen in single-shot imaging data obtained via the configuration density technique. Numerical results for larger systems of N=15 and 30 particles show that the crystalline configurations observed are not the same as the classical Wigner crystal structures that emerge should the confined charged particles interact with a Coulomb potential. An important question floated is whether such crystalline structures do really exist in a quantum system or whether they are artifacts of the methods used to analyze them.