Phonon frequencies from path integral quantum correlators in strongly anharmonic systems*

The recent discovery of high-temperature high-pressure superconductivity in H3S and LaH10 reveals the fundamental role played by hydrogen in making these materials superconducting. The solid state of pristine hydrogen has been the object of intense research, in quest of a metallic phase which could superconduct at room temperature.

As hydrogen is the lightest element, the key feature of hydrogen-rich materials is the presence of strong proton fluctuations. In order to take them into account in ab initio calculations, one should go beyond the harmonic framework. This is essential to determine the electron-phonon coupling which should drive the system into the superconducting state.

In this work we propose a zero-time Kubo-correlator, built upon path integral Molecular Dynamics trajectories, which yields very accurate anharmonic renormalizations of phonon frequencies. We benchmark our approach against exactly solvable 1-dimensional and 2-dimensional models, and we present new results for the atomic I41/amd phase and for the molecular phase III of high-pressure solid hydrogen.