Quantifying exchange effects in incommensurate solid 4He

In this paper, we use path-integral Monte Carlo (PIMC) simulations to study how the permutation effect, a specific quantum exchange phenomenon, affects the stability of incommensurate solid 4He with vacancy defects. By comparing simulations within Bose and Boltzmann statistics, we isolate the effects of quantum exchange. We examine the solids with densities from 0.028 to 0.035 & Aring;-3 and vacancy concentrations from 0.55 to 5.55% in the temperature range 0.2-2.0 K. The calculations show that permutations reduce the vacancy formation energy by up to 19%, especially at lower densities. Vacancies in the studied concentration range can lead to lattice distortions with a reduction in the local density of 1% to 5% and a compensatory increase in the neighboring regions. The Bose statistics influence the local atomic arrangement, which is reflected in the pair-correlation function, with the peaks and valleys changing by about 2% at larger distances. Permutation effects on the vacancy formation energy show a dependence on density and temperature with "steplike behavior". Our results demonstrate that quantum statistics play a significant role in shaping the structure and stability of solid 4He-containing vacancies.