Elastic constants of quantum solids by path integral simulations

Two methods are proposed to evaluate the second-order elastic constants of quantum mechanically treated solids. One method is based on path-integral simulations in the NVT ensemble using an estimator for elastic constants Ci j . The other method is based on simulations in the NpT ensemble exploiting the relationship between strain fluctuations and elastic constants. The strengths and weaknesses of the methods are discussed thoroughly. We show how one can reduce statistical and systematic errors associated with so-called primitive estimators. The methods are then applied to solid argon at atmospheric pressures and solid helium 3 ~hcp, fcc, and bcc! under varying pressures. Good agreement with available experimental data on elastic constants is found for He. Predictions are also made for the thermal expectation value of the kinetic energy of solid He.