Accurate Density Response Function of Superfluid 4He at Freezing Pressure: Is DFT Successful for Superfluid Freezing?

An accurate density response function χ(q) of superfluid 4He at zero temperature and at freezing pressure, up to about q=8 A−1, has been obtained via dynamic structure factors, S(q,ω), extracted from imaginary time density–density correlation functions computed with an exact Path Integral projector method. A new statistical approach (Vitali et al. in Phys. Rev. B 82:174510, 2010) to inverse problems has been used to extract S(q,ω); contrarily to analogous “analytic continuation” approaches, this new method has been found able to separate a well defined elementary excitation peak from multi–phonon contributions. We have applied density functional theory (DFT) to a superfluid–solid transition with the obtained χ(q). With this accurate input, DFT gives unphysically unstable superfluid against solidification which is consistent with conventional works. We discuss the possible defect of DFT.