Phonons of solid atomic Hydrogen with quantum Monte Carlo

The calculation of phonon frequencies and modes is the starting point for investigating a variety of physical properties of solids, like the specific heat, thermal expansion, and properties related to electron-phonon coupling, like superconductivity. For solid Hydrogen at high pressures, the zero point motion of the protons is known to be important when determining its structures. This effect can be accounted for if the phonon frequencies are known. These calculations are routinely carried out with density functional theory (DFT). Here, we calculate the phonons of solid atomic Hydrogen with quantum Monte Carlo (QMC), a feat made possible by the calculation of forces in QMC, highly optimized wavefunctions, and careful attention to statistical error. We compare the results with those obtained within DFT.