Probing anharmonic phonons by quantum correlators: A path integral approach

TL;DR

This paper introduces a novel method using Path Integral Molecular Dynamics to accurately determine anharmonic phonon spectra, capturing quantum and temperature effects, and demonstrates its effectiveness on real materials like diamond and atomic hydrogen.

Contribution

It develops two estimators based on PIMD correlation functions for fully characterizing phonon spectra and anharmonicity, with improved computational efficiency through generalized eigenvalue equations.

Findings

Accurate phonon spectra for diamond and atomic hydrogen obtained.

Anharmonicity in atomic hydrogen is stronger than previously thought.

The method achieves faster convergence and reduces time-step bias.

Abstract

We devise an efficient scheme to determine vibrational properties from Path Integral Molecular Dynamics (PIMD) simulations. The method is based on zero-time Kubo-transformed correlation functions and captures the anharmonicity of the potential due to both temperature and quantum effects. Using analytical derivations and numerical calculations on toy-model potentials, we show that two different estimators built upon PIMD correlation functions fully characterize the phonon spectra and the anharmonicity strength. The first estimator is associated with force-force quantum correlators and gives access to the fundamental frequencies and thermodynamic properties of the quantum system. The second one is instead connected to displacement-displacement correlators and probes the lowest-energy phonon excitations with high accuracy. We also prove that the use of generalized eigenvalue equations, in place of the standard normal mode equations, leads to a significant speed-up in the PIMD phonon calculations, both in terms of faster convergence rate and smaller time-step bias. Within this framework, using ab initio PIMD simulations, we compute phonon dispersions of diamond and of the high-pressure I41/amd phase of atomic hydrogen. We find that, in the latter case, the anharmonicity is stronger than previously estimated and yields a sizeable red-shift in the vibrational spectrum of atomic hydrogen.