Revisiting the Broken Symmetry Phase of Solid Hydrogen: A Neural Network Variational Monte Carlo Study

The crystal structure of high-pressure solid hydrogen remains a fundamental open problem. Although the research frontier has mostly shifted toward ultra-high pressure phases above 400 GPa, we show that even the broken symmetry phase observed around 130~GPa requires revisiting due to its intricate coupling of electronic and nuclear degrees of freedom. Here, we develop a first principle quantum Monte Carlo framework based on a deep neural network wave function that treats both electrons and nuclei quantum mechanically within the constant pressure ensemble. Our calculations reveal an unreported ground-state structure candidate for the broken symmetry phase with Cmcm space group symmetry, and we test its stability up to 96 atoms. The predicted structure quantitatively matches the experimental equation of state and gives the closest x-ray diffraction peak-position match among the tested candidates. Furthermore, our group-theoretical analysis provides a symmetry-counting compatibility check between the Cmcm structure and existing Raman and infrared spectroscopic data. Crucially, static density functional theory calculation reveals the Cmcm structure as a dynamically unstable saddle point on the Born-Oppenheimer potential energy surface, demonstrating that a full quantum many-body treatment of the problem is necessary. These results shed new light on the phase diagram of high-pressure hydrogen and call for further experimental verifications.