Quantifying exchange effects in incommensurate solid He4

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 ^-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.