Trial wave functions for High-Pressure Metallic Hydrogen

Many body trial wave functions are the key ingredient for accurate Quantum Monte Carlo estimates of total electronic energies in many electron systems. In the Coupled Electron-Ion Monte Carlo method, the accuracy of the trial function must be conjugated with the efficiency of its evaluation. We report recent progress in trial wave functions for metallic hydrogen implemented in the Coupled Electron-Ion Monte Carlo method. We describe and characterize several types of trial functions of increasing complexity in the range of the coupling parameter $1.0 \leq r_s \leq1.55$. We report wave function comparisons for disordered protonic configurations and preliminary results for thermal averages.