High-pressure hydrogen with neural quantum states

We employ neural quantum states to model the ground state of dense hydrogen, including both electronic and protonic degrees of freedom. Our trial wave function achieves lower Born-Oppenheimer energies than prior projector Monte Carlo methods in the atomic phase for systems up to 128 atoms. By incorporating nuclear quantum effects, we avoid any explicit symmetry assumption on the expected quantum crystal. As a first application, we investigate pressure-induced melting in an extremely high-density region. We further present improved force and pressure estimators that can not only be used to systematically extend our understanding of the hydrogen phase diagram, but that can be applied more broadly to other systems.