Anharmonicity and Coulomb pseudopotential effects on superconductivity in YH$_6$ and YH$_9$

Anharmonic effects are widely believed to be the primary cause of the overestimation of superconducting transition temperatures of yttrium hydrides YH$_6$ and YH$_9$ in theoretical predictions. However, prior studies indicate that anharmonicity alone may be insufficient to account for this discrepancy. In this work, we employ the stochastic path-integral approach to investigate the quantum and anharmonic effects of ions in yttrium hydrides. Our calculations reveal significant corrections to the electron-phonon coupling parameters and an increase in the average phonon frequency compared to density functional perturbation theory, aligning closely with results from the stochastic self-consistent harmonic approximation. We find that properly taking into account the renormalization of the Coulomb pseudopotential due to the frequency cutoff, which is often overlooked in previous calculations, is critical to predicting transition temperatures consistent with experimental values for both YH$_6$ and YH$_9$. This indicates that, with this correction, anharmonic effects are sufficient to explain the discrepancies between experimental and theoretical results.