  We conduct a theoretical study in which we determine the zero-point vacancy
concentration in solid 4He at T=0 K. To this end, we employ the
quantum-classical isomorphism, by which the quantum-mechanical probability
density function of a system composed of bosons at T=0K can be interpreted in
terms of a Boltzmann factor of a classical system at finite temperature. By
using this classical isomorph we apply the methods of classical statistical
mechanics to compute the vacancy formation free energy and the vacancy
concentration in the associated quantum system at T=0. In this context, we
focus specifically on the role of anharmonic effects that are expected to be
non-negligible due to the significant zero-point motion. For this purpose, we
compute the formation free energies using both the harmonic approximation (HA)
as well as reversible-work (RW) method, in which all anharmonic effects are
taken into account. The results suggest that anharmonic effects indeed play a
significant role, lowering the classical formation free energy by ~25% and
increasing the zero-point vacancy concentration by more than an order of
magnitude compared to the HA.
