Unveiling the phase diagram of high-pressure Hydrogen

Production of metallic hydrogen is one of the top three open quests of physics[1]. Three different experimental groups claim to have obtained metallic hydrogen at different pressures, with contradicting results. The firsts [2, 3] measured a transition from phase III to a new insulator molecular phase at 360 GPa, then to a shiny metallic phase at 490 GPa. Another work[4] showed how phase III becomes a metal through indirect bandgap closure at about 360 GPa and it remains stable up to at least 440 GPa. Lastly, a different work[5] measured the infrared transmission up to 430 GPa, claiming that phase III transforms to a new metallic state at about 420 GPa through a first-order phase transition. In this scenario, experimental data need the support from theoretical simulations to correctly understand the hydrogen phase- diagram, as experiments provide only indirect measurements: optical absorption, reflectivity, and vibrational spectroscopy. In this thesis, I feature the paramount role played by nuclear quantum fluctua- tions in the phase-diagram and the optical and vibrational properties of high-pressure hydrogen. In the first part of the thesis, I develop a new technique to simulate the quantum character of nuclei, able to correctly describe both phonon-phonon and electron-phonon interactions. In this way, the crystal structure can be relaxed, including lattice parameters, considering quantum and thermal fluctuations. By optimizing also the lattice with quantum fluctuations, I discover new crystalline structures, good candidates for high pressure hydrogen phases. Thanks to the advances I introduce here, it is possible to simulate the anharmonic IR and Raman spectra with phonon lifetimes, allowing for an unprecedented theoretical accuracy, enabling the direct comparison with experiments. I simulate also the optical proper- ties of the high-pressure hydrogen, including the electron-phonon interaction. By computing the direct and indirect bandgap closure of phase III, I conciliate the apparent contradicting scenario revealed by experiments[4, 5].