Optimal configurations and "Pauli crystals" of quantum clusters

TL;DR

This paper introduces an algorithm to determine optimal configurations of quantum clusters from density images, revealing geometric patterns called 'Pauli crystals' across different quantum gases and identifying phase transitions.

Contribution

The study develops a novel algorithm that finds optimal quantum cluster configurations directly from density data, applicable to interacting gases and independent of particle statistics.

Findings

Successfully recovers exact configurations of quantum clusters.

Identifies phase transitions through changes in optimal configurations.

Demonstrates applicability to both Bose and Fermi gases.

Abstract

Broken rotational and translational symmetries are the hallmarks of solid state materials. In contrast, quantum liquids and gases do not exhibit such properties. However, if we regard the logarithm of the absolute square of a quantum liquid as an energy ${\cal E}= -{\rm ln}|\Psi|^2$, a geometric pattern naturally occurs at the minimum, i.e. the optimal configuration. Such geometric patterns have recently been studied for non-interacting fermions, and have been named "Pauli crystals". However, such patterns exist in all interacting gases (Bose or Fermi), independent of statistics. Here, we present an algorithm to determine the optimal configurations of quantum clusters solely from the images of their densities and without theoretical inputs. We establish its validity by recovering a number of exact results, showing that it can identify the changes in the cluster's ground state which corresponds to phase transitions in bulk systems.