Density-Functional Theory of Quantum Freezing: Sensitivity to Liquid-State Structure and Statistics

TL;DR

This paper applies density-functional theory to study quantum freezing in Bose and Fermi hard-sphere solids, analyzing how liquid-state structure and statistics influence the ground-state energies and phase transitions.

Contribution

It introduces a method combining the weighted-density approximation and phonon analysis to model quantum solids, including Fermi systems with antisymmetry effects, without adjustable parameters.

Findings

Quantum hard-sphere solids' energies computed with no adjustable data.

Predicted liquid-solid transition points align qualitatively with simulations.

Identifies limitations of the Feynman approximation, suggesting need for improved liquid-state input.

Abstract

Density-functional theory is applied to compute the ground-state energies of quantum hard-sphere solids. The modified weighted-density approximation is used to map both the Bose and the Fermi solid onto a corresponding uniform Bose liquid, assuming negligible exchange for the Fermi solid. The required liquid-state input data are obtained from a paired phonon analysis and the Feynman approximation, connecting the static structure factor and the linear response function. The Fermi liquid is treated by the Wu-Feenberg cluster expansion, which approximately accounts for the effects of antisymmetry. Liquid-solid transitions for both systems are obtained with no adjustment of input data. Limited quantitative agreement with simulation indicates a need for further improvement of the liquid-state input through practical alternatives to the Feynman approximation.