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$LaH_{10}$, as a member of hydrogen-rich superconductors, has asuperconducting critical temperature of 250 K at high pressures, which exhibitsthe possibility of solving the long-term goal of room temperaturesuperconductivity. Considering the extreme pressure and low mass of hydrogen,the nuclear quantum effects in $LaH_{10}$ should be significant and have animpact on its various physical properties. Here, we adopt the method combinesdeep-potential (DP) and quantum thermal bath (QTB), which was verified to beable to account for quantum effects in high-accuracy large-scale moleculardynamics simulations. Our method can actually reproduce pressure-temperaturephase diagrams of $LaH_{10}$ consistent with experimental and theoreticalresults. After incorporating quantum effects, the quantum fluctuation drivendiffusion of proton is found even in the absence of thermal fluctuation near 0K. The high mobility of proton is found to be compared to liquid, yet thestructure of $LaH_{10}$ is still rigid. These results would greatly enrich ourvision to study quantum behavior of hydrogen-rich superconductors.

Zero-Point Quantum Diffusion of Proton in Hydrogen-rich Superconductor $LaH_{10}$