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

TL;DR

This study employs a neural network variational Monte Carlo approach to identify a new candidate structure for the broken symmetry phase of solid hydrogen at 130 GPa, aligning with experimental data and emphasizing the importance of quantum many-body effects.

Contribution

It introduces a first-principles quantum Monte Carlo framework with neural networks to accurately model electron-nuclear coupling in high-pressure hydrogen phases.

Findings

Identifies a new $Cmcm$ structure candidate for the broken symmetry phase.

Matches experimental equation of state and diffraction data.

Shows static DFT finds the structure dynamically unstable, highlighting the need for quantum many-body treatment.

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 X-ray diffraction patterns. Furthermore, our group-theoretical analysis shows that the $Cmcm$ structure is compatible with 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.