<i>Ab initio</i> calculation of atomic solid hydrogen phases based on Gutzwiller many-body wave functions

We apply two<i>ab initio</i>many-body methods based on Gutzwiller wave functions, i.e., correlation matrix renormalization theory (CMRT) and Gutzwiller conjugate gradient minimization (GCGM), to the study of crystalline phases of atomic hydrogen. Both methods avoid empirical Hubbard<i>U</i>parameters and are free from double-counting issues. CMRT employs a Gutzwiller-type approximation that enables efficient calculations, while GCGM goes beyond this approximation to achieve higher accuracy at higher computational cost. By benchmarking against available quantum Monte Carlo (QMC) results, we demonstrate that while both methods are more accurate than the widely used density-functional theory, GCGM systematically captures additional correlation energy missing in CMRT, leading to significantly improved total energy predictions. We also show that by including the correlation energyEcfrom local density approximation in the CMRT calculation, CMRT +Ecproduces energy in better agreement with the QMC results in these hydrogen lattice systems.