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

Abstract: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.

Strongly Correlated Electrons (cond-mat.str-el); Materials Science (cond-mat.mtrl-sci); Machine Learning (cs.LG); Computational Physics (physics.comp-ph)

arXiv:2512.17703 [cond-mat.str-el]

(or arXiv:2512.17703v3 [cond-mat.str-el] for this version)

Phys. Rev. B 114, 225102 (2026)

https://doi.org/10.1103/t4bd-347y DOI(s) linking to related resources