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 the force–force quantum correlators and, in the weak anharmonic regime, yields reliable zero-point motion frequencies and thermodynamic properties of the quantum system. The second one is instead connected to displacement–displacement correlators and accurately probes the lowest-energy phonon excitations, regardless of the anharmonicity strength of the system. 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.

The breaking of time-reversal symmetry (TRS) in the normal state of kagome superconductors AV₃Sb₅ stands out as a significant feature, but its tunability is unexplored. Using low-energy muon spin rotation and local field numerical analysis, we study TRS breaking as a function of depth in single crystals of RbV₃Sb₅ (with charge order) and Cs(V_0.86Ta_0.14)₃Sb₅ (without charge order). In the bulk of RbV₃Sb₅ (>33 nm from the surface), we observed an increase in the internal magnetic field width in the charge-ordered state. Near the surface (<33 nm), the muon spin relaxation rate is significantly enhanced and this effect commences at temperatures significantly higher than the onset of charge order. In contrast, no similar field width enhancement was detected in Cs(V_0.86Ta_0.14)₃Sb₅, either in the bulk or near the surface. These observations indicate a strong connection between charge order and TRS breaking and suggest that TRS breaking can occur prior to long-range charge order.

We devise a framework to compute accurate phonons in molecular crystals even in case of strong quantum anharmonicity. Our approach is based on the calculation of the static limit of the phononic Matsubara Green's function from path integral molecular dynamics simulations. Our method enjoys a remarkably low variance, which allows one to compute accurate phonon frequencies after a few picoseconds of nuclear dynamics, and it is further stabilized by the use of appropriate constrained displacement operators. We applied it to solid hydrogen at high pressure. For phase III, our predicted infrared (IR) and Raman active vibrons agree very well with experiments. We then characterize the crystalline symmetry of phase IV by direct comparison with vibrational data and we determine the character and isotopic shift of its Raman and IR vibron peaks.

We study the structural phase transition, originally associated with the highest superconducting critical temperature T_c measured in high-pressure sulfur hydride. A quantitative description of its pressure dependence has been elusive for any ab initio theory attempted so far, raising questions on the actual mechanism leading to the maximum of T_c. Here, we estimate the critical pressure of the hydrogen bond symmetrization in the Im $$\bar{3}$$3 ¯ m structure, by combining density functional theory and quantum Monte Carlo simulations for electrons with path integral molecular dynamics for quantum nuclei. We find that the T_c maximum corresponds to pressures where local dipole moments dynamically form on the hydrogen sites, as precursors of the ferroelectric Im $$\bar{3}$$3 ¯ m-R3m transition, happening at lower pressures. For comparison, we also apply the self-consistent harmonic approximation, whose ferroelectric critical pressure lies in between the ferroelectric transition estimated by path integral molecular dynamics and the local dipole formation. Nuclear quantum effects play a major role in a significant reduction (≈50 GPa) of the classical ferroelectric transition pressure at 200 K and in a large isotope shift (≈25 GPa) upon hydrogen-to-deuterium substitution of the local dipole formation pressure, in agreement with the corresponding change in the T_c maximum location.