Density-functional theory of freezing of quantum liquids at zero temperature using exact liquid-state linear response

TL;DR

This paper uses exact linear response data within density functional theory to analyze the freezing of quantum liquids at zero temperature, revealing limitations of current approximations in three dimensions.

Contribution

It demonstrates that existing density functional approximations fail to accurately predict 3D quantum freezing due to incorrect response function behavior.

Findings

Exact response functions differ significantly at large wavevectors.

Current density functional theories are inadequate for 3D quantum freezing.

Accurate linear response data improves understanding of effective interactions in electron gases.

Abstract

We apply density functional theory to study the freezing of superfluid {$^{4}\rm{He}$}, charged bosons and charged fermions at zero temperature. We employ accurate Quantum Monte Carlo data for the linear response function in the uniform phase of these systems, a quantity that has different behavior for large values of the wavevector than previously assumed. We find that, as a result of this {\it{exact}} behavior, different approximations in the density functional theory of freezing that involve linear response, all fail to correctly describe the crystallization in {\it{three dimensions}}, while yielding satisfactory predictions in {\it{two dimensions}}. This demonstrates the shortcomings of the currently popular density functional approximate theories to describe $3d$-freezing in the quantum regime. We also investigate the consequences of the exact asymptotic behavior of response functions on the form of effective interactions and polarization potentials in the electron gas, at small distances.