  Solid atomic hydrogen is one of the simplest systems to undergo a
metal-insulator transition. Near the transition, the electronic degrees of
freedom become strongly correlated and their description provides a difficult
challenge for theoretical methods. As a result, the order and density of the
phase transition are still subject to debate. In this work we use diffusion
quantum Monte Carlo to benchmark the transition between paramagnetic and
anti-ferromagnetic body centered cubic atomic hydrogen in its ground state. We
locate the density of the transition by computing the equation of state for
these two phases and identify the phase transition order by computing the band
gap near the phase transition. These benchmark results show that the phase
transition is continuous and occurs at a Wigner-Seitz radius of $r_s=2.27(3)
a_0$. We compare our results to previously reported density functional theory,
Hedin's GW approximation, and dynamical mean field theory results.

Strongly Correlated Electrons