Density functional theory and Bose statistics for the freezing of superfluid 4He

Density functional theory so far has experienced pathological results in the description of the freezing of superfluid 4He, even with the use of accurate inputs, namely the density response function, χ(q), and the equation of state of the superfluid. In fact, while the second order approximation of Ramakrishnan-Yussouff type gives a too much stable solid phase (Likos et al. in Phys. Rev. B 55:8867, 1997; Minoguchi and Galli in J. Law Temp. Phys. 162:160, 2011), a non-perturbative treatment called modified weighted density approximation (MWDA) gives, on the other hand, a too stable superfluid phase (Minoguchi et al. in J. Phys. Conf. Ser. 2012). We have preliminarily performed a MWDA calculation for a specific Gaussian distortion α=0.387 Å−2 of liquid 4He. By using χ(q) and the equation of state of a system of liquid 4He in which Bose statistics has been suppressed, we have found that the calculation provides a lower energy. This indicates that the solid may be better described by a distorted normal liquid. The input data has been obtained via Path Integral Monte Carlo simulations of a system of distinguishable 4He atoms. The χ(q) has been obtained from the dynamic structure factors extracted, via the Genetic Inversion via Falsification of Theories (GIFT) method (Vitali et al. in Phys. Rev. B 82:174510, 2010) from imaginary time density–density correlation functions.