Microscopic studies of solid 4He with Path Integral Projector Monte Carlo

TL;DR

This study uses the Shadow Path Integral Ground State method to analyze the quantum properties of solid helium-4, revealing insights into Bose-Einstein condensation, grain boundary effects, and vacancy concentrations at zero temperature.

Contribution

It introduces an exact projector method for quantum solids, improves off-diagonal property sampling, and estimates vacancy concentrations and condensate fractions in solid helium-4.

Findings

Condensate fraction in bulk solid 4He is extremely low, with an upper bound of 2.5×10^-8.

Finite condensate fractions are found at grain boundaries in the crystal.

Estimated vacancy concentration at melting density is approximately 0.0014.

Abstract

We have investigated the ground state properties of solid $^4$He with the Shadow Path Integral Ground State method. This exact T=0 K projector method allows to describes quantum solids without introducing any a priori equilibrium position. We have found that the efficiency in computing off-diagonal properties in the solid phase sensibly improves when the direct sampling of permutations, in principle not required, is introduced. We have computed the exact one-body density matrix (obdm) in large commensurate 4He crystal finding a decreasing condensate fraction with increasing imaginary time of projection, making our result not conclusive on the presence of Bose-Einstein condensation in bulk solid 4He. We can only give an upper bound of 2.5 times 10^-8 on the condensate fraction. We have exploited the SPIGS method to study also 4He crystal containing grain boundaries by computing the related surface energy and the obdm along these defects. We have found that also highly symmetrical grain boundaries have a finite condensate fraction. We have also derived a route for the estimation of the true equilibrium concentration of vacancies x_v in bulk T=0 K solid 4He, which is shown to be finite, x_v=0.0014(1) at the melting density, when computed with the variational shadow wave function technique.