Freezing of helium-4: Comparison of different density functional approaches

Solidification of superfluid helium-4 has been addressed within the framework of density functional theory. Early studies used a variational approach, approximating the density distribution in the solid phase by a sum of Gaussians on each lattice site. Recently, we performed an unconstrained minimization of the functional describing the helium system as reported by Ancilotto et al. (Phys. Rev. B, 72, 214522, 2005). At sufficiently high density, we find stable solid like solutions, which exhibit an anisotropic density profile around each lattice site. We compare these results to the previous variational approach, and attempt to improve the family of trial functions by adding a variational parameter to account for anisotropy.