Correlation Matrix Method for Phonon Quasiparticles

Abstract

Phonon anharmonicity is ubiquitous in real materials and is crucial for understanding thermal properties and phase stability. In this work, we show that anharmonic phonon modes can be obtained by maximizing their vibration stability during fitting the atomic trajectory. We prove that all information about these quasiparticles is contained in two small correlation matrices $\mathcal{S}$ and $\mathcal{Q}$, which can be constructed directly from molecular dynamics simulations. Based on these matrices, we proposed an optimization scheme, which allows us to efficiently determine temperature-dependent phonon modes along with their frequencies and lifetimes. We verified this method by applying it to silicon and cubic CaSiO$_3$, where it successfully captured their temperature-dependent phonon behaviors and the well-known phonon softening in cubic CaSiO$_3$. This theory provides a convenient tool for investigating phonon quasiparticles and can be extended to study other quasiparticles, such as electrons, holes, and magnons.