Influence of Anharmonic Effects on the Zero-point Vacancy Concentration in Solid 4He

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.