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

Density-functional theory is applied to compute the groundstate energies of quantum hard-sphere solids. The modified weighteddensity 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, combined with an enhanced hypernetted-chain integral equation, 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, the Fermi liquid freezing at lower density than the Bose liquid because of the destabilizing influence of fermionic statistics. Predictions for these quantum systems are shown to be more sensitive to the accuracy of the input data than is the case for the classical counterpart. Limited quantitative agreement with simulation indicates a need for still further improvement of the liquid-state input, likely through practical alternatives to the Feynman approximation. Date: 7 February 2008 PACS number(s): 64.70.Dv, 05.70.-a, 64.60.-i, 67.80.-s * Present address: Institut für Festkörperforschung, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany ([email protected])