Elastic constants of hcp $^{4}$He: Path-integral Monte Carlo results versus experiment

TL;DR

This study uses path-integral Monte Carlo simulations to calculate the elastic constants of hcp $^{4}$He, comparing results with experimental data and exploring phase differences, providing insights into quantum solid behavior.

Contribution

The paper introduces a new PIMC-based method to compute elastic constants of quantum solids and compares these with experimental results, highlighting phase-dependent agreement.

Findings

Good agreement with experimental elastic constants for hcp $^{4}$He, except for C$_{13}$.

Excellent agreement for all elastic constants in the bcc phase.

Development of a stress tensor expression for PIMC simulations.

Abstract

The elastic constants of hcp $^{4}$He are computed using the path-integral Monte Carlo (PIMC) method. The stiffness coefficients are obtained by imposing different distortions to a periodic cell containing 180 atoms, followed by measurement of the elements of the corresponding stress tensor. For this purpose an appropriate path-integral expression for the stress tensor observable is derived and implemented into the PIMC++ package. In addition to allowing the determination of the elastic stiffness constants, this development also opens the way to an explicit atomistic determination of the Peierls stress for dislocation motion using the PIMC technique. A comparison of the results to available experimental data shows an overall good agreement of the density dependence of the elastic constants, with the single exception of C$_{13}$. Additional calculations for the bcc phase, on the other hand, show good agreement for \textit{all} elastic constants.