Probing anharmonic phonons by quantum correlators: A path integral approach

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.

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Cited by in corpus (7)

• Quantum phase diagram of high-pressure hydrogen
• Mode-coupling theory of lattice dynamics for classical and quantum crystals
• Phonons of metallic hydrogen with quantum Monte Carlo
• Stability and distortion of fcc-LaH${}_{10}$ with path-integral molecular dynamics
• High-pressure II-III phase transition in solid hydrogen: Insights from state-of-the-art ab initio calculations
• Reciprocal space temperature-dependent phonons method from ab-initio dynamics
• Hydrogen phase-IV characterization by full account of quantum anharmonicity