Elastic moduli and thermal conductivity of quantum materials at finite temperature

We describe a theoretical and computational approach to calculate the vibrational, elastic, and thermal properties of materials from the low-temperature quantum regime to the high-temperature anharmonic regime. This approach is based on anharmonic lattice dynamics and the Boltzmann transport equation. It relies on second and third-order force constant tensors estimated by fitting temperature-dependent empirical potentials (TDEP) from path-integral quantum simulations with a first-principles machine learning Hamiltonian. The temperature-renormalized harmonic force constants are used to calculate the elastic moduli and the phonon modes of materials. Harmonic and anharmonic force constants are combined to solve the phonon Boltzmann transport equation to compute the lattice thermal conductivity. We demonstrate the effectiveness of this approach on bulk crystalline silicon in the temperature range from 50 to 1200~K, showing substantial improvement in the prediction of the temperature dependence of the target properties compared to experiments.