Monte Carlo simulations of high pressure hydrogen

The aim of this Ph.D. thesis is the study of high pressure hydrogen phases, by means of Monte Carlo simulations, both on effective models and from ab initio simulations. The determination of the physical properties of hydrogen under extreme conditions is of fundamental importance in Astrophysics and Planetary Science to build models describing i.e. brown dwarfs, stars, giant planets, systems mainly composed by hydrogen. More generally in the field of the Condensed Matter Physics, the interest on high pressure hydrogen was originated by the Wigner and Hungtington prediction on the possible occurrence of a metallization transition in low temperature solids, driven by the pressure. The experimental compression techniques (static and dynamic) have depicted for hydrogen a phase diagram of unexpected richness. However, the region of the phase diagram in which the most interesting transitions occur is not accessible through experiments. The ab initio simulation techniques are then a fundamental tools to extend our knowledge on hydrogen at extreme pressures. The most of the simulations are carried out with Born-Oppenheimer (BO) methodologies based on the Density Functional Theory (DFT) evaluation of the electronic ground state at a given nuclear configuration. The accuracy of these simulations is however limited near the metallization transition, due to the well known DFT tendency to favor the metallic versus the insulating states. Recently an alternative approach has been developed, still within the BO approximation: the Coupled Electron-Ion Monte Carlo method, entirely based on MC algorithms, applied both to electrons and nuclei. This method, not suffering of the DFT limitations, may be able to provide accurate results over the entire phase diagram. This thesis is organized as follows. In Chapter 1 we introduce to the problem of the high pressure hydrogen, describing in detail the different regions of the phase diagram reconstructed so far through experiments and numerical simulations. In Chapter 2 we present the theoretical framework of this thesis. After a general discussion of the different Monte Carlo techniques applied in this work (Metropolis Monte Carlo for classical particles, Path Integral Monte Carlo for quantum particles at finite temperature, Variational and Reptation Quantum Monte Carlo for quantum ground state calculations), the Coupled Electron-Ion Monte Carlo method is presented. The the electronic wave functions adopted in the simulations and the wave function optimization procedure are described too. The remaining Chapters are devoted to the results of this work. Chapter 3 concerns the effective screened Coulomb system. It presents a short derivation of the screened Coulomb pair potential and the discussion of the results on the classical system and of the quantum correction to the classical melting line. In Chapter 4 we present the results of the CEIMC simulation on hydrogen in the atomic phase. The first part of this chapter deals with the study at T = 0K of several crystal structures for the atomic hydrogen. The last part concerns the finite temperature study of the stability of the solid vs. the liquid phase. Finally, in Chapter 5 we discuss our results on the liquid-liquid transition.