2021/07/22 by Tin-Lun Ho, Ho, Tin-Lun, Saad Khalid +1
Physics and Astronomy · #FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas) #cond-mat.quant-gas
paper · pdf · doi:10.48550/arxiv.2107.10949
Combined file of manuscript and supplementary materials. 5 figures in main text, 2 figures in supplementary materials
arxiv created 2021/07/22 · arxiv updated 2021/07/26
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|Ψ|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.