Self-consistent phonon (SCP) theory and its application in computing thermodynamic properties of materials are reviewed from a historical perspective. Various more recent implementations based on first-principles electronic structure methods using the density functional theory (DFT) have been discussed. The SCP equations can be derived either from a diagrammatic perturbation theory or a variational approach based on free-energy minimization. These methods can also be used to predict phase change due to phonon softening, and can be extended to study the coupling of phonons to other degrees of freedom in the system.
@article{arxiv.1911.00787,
title = {Thermodynamics of anharmonic lattices from first-principles},
author = {Keivan Esfarjani and Yuan Liang},
journal= {arXiv preprint arXiv:1911.00787},
year = {2019}
}