A quantum Monte Carlo study of high pressure solid and liquid hydrogen

Hydrogen is the first element of the periodic table. As such, it is often regarded as the simplest one: the non-relativistic hydrogen atom is a problem exactly solved in many textbooks; the hydrogen molecular ion H 2 + and the diatomic molecule H 2 are, correspondingly, the first systems to be considered when more than one nucleus is involved. As a thermodynamic system, its phase diagram at low pressures is quite standard: at room temperature and ambient pressure, hydrogen is a molecular fluid; upon cooling, it becomes a molecular solid; its critical point is T=33 K and P=1.3 Pa. Nevertheless, even such a simple system becomes really interesting when pressure is increased by several orders of magnitude. Speculations about the existence of a metallic solid state at 25 GPa and 0 K temperature started with Wigner and Huntington; later calculations suggested that this state could become a high-temperature superconductor . When experiments achieved the predicted transition temperature, they did not find a metallic state; on the other hand, they found a rich phase diagram, where several different solid phases exist. Nowadays, the quest for solid metallic hydrogen at low temperature is still an on-going activity. As temperature is increased above ≈ 1000 K, the system enters the liquid phase: it is important to obtain an accurate equation of state at high temperature and high pressure, in order to model the properties of gas giants, such as Jupiter and Saturn, which are mostly made of hydrogen and helium. Metallic hydrogen, which is yet to be seen in the solid state, was experimentally measured in the liquid phase. Performing experiments at such high pressures is complicated; the information obtained is partial. At low temperatures, the boundaries among the different solid phases can be drawn, but most of their structural properties are still an open problem; at high temperatures, characterizing the insulator-metal transition is hard because of large uncertainties and conflicting results. Ab Initio simulations can be a valuable tool to complement and interpret experimental data; they can also guide experiments with their predictive power. For condensed matter, Density Functional Theory (DFT) is the method of choice to perform Ab Initio simulations at reasonable computational cost. However, their predictive power for high pressure hydrogen is questioned due to several levels of approximation which will be discussed in our work: in particular, the fact that DFT is plagued by an uncontrolled approximation (the exchange-correlation functional approximation) will be elaborated. iiiIn this thesis, we will employ a different method to run Ab Initio simulations of high pressure hydrogen at finite temperature: the Coupled Electron Ion Monte Carlo (CEIMC). We will discuss how CEIMC, combining the Path Integral formalism to treat the nuclear degrees of freedom and the Variational Monte Carlo (VMC) method to accurately compute electronic energies in a Born-Oppenheimer framework, can perform finite temperature simulations without suffering from the same kind of uncontrolled approximation which plagues DFT. We will then apply the method to the low temperature, solid phase and to the high-temperature, liquid one. In the first case, finite temperature simulations of different candidate structures for the various solid phases will be performed, comparing CEIMC results with DFT ones. In the second case, the liquid-liquid phase transition will be investigated, drawing attention to the relationship between molecular dissociation and metallization; to do so, the system will be characterized across the transition with the computation of relevant optical properties.