  We present a first-principles computational study of solid 4He at T=0K and
pressures up to 160GPa. Our computational strategy consists in using van der
Waals density functional theory (DFT-vdW) to describe the electronic degrees of
freedom in this material, and the diffusion Monte Carlo (DMC) method to solve
the Schrodinger equation describing the behavior of the quantum nuclei. For
this, we construct an analytical interaction function based on the pairwise
Aziz potential that closely matches the volume variation of the cohesive energy
calculated with DFT-vdW in dense helium. Interestingly, we find that the
kinetic energy of solid 4He does not increase appreciably with compression for
P > 85GPa. Also, we show that the Lindemann ratio in dense solid 4He amounts to
0.10 almost independently of pressure. The reliability of customary
quasi-harmonic DFT (QH DFT) approaches in the description of quantum nuclear
effects in solids is also studied. We find that QH DFT simulations, although
provide a reasonable equation of state in agreement with experiments, are not
able to reproduce correctly these critical effects in compressed 4He. In
particular, we disclose huge discrepancies of at least ~50% in the calculated
4He kinetic energies using both the QH DFT and present DFT-DMC methods.
