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.

翻译：高压固态氢的晶体结构仍是一个基本的开放性问题。尽管研究前沿已大多转向400 GPa以上的超高压相，但我们指出，即使在约130 GPa处观测到的破缺对称相，由于其电子与核自由度之间复杂的耦合，也需要重新审视。本文中，我们开发了一个基于深度神经网络波函数的第一性原理量子蒙特卡洛框架，该框架在恒压系综中对电子和原子核均进行量子力学处理。我们的计算揭示了一个先前未报道的、具有$Cmcm$空间群对称性的破缺对称相基态结构候选，并在多达96个原子的体系中测试了其稳定性。该预测结构在定量上与实验状态方程和X射线衍射图谱相符。此外，我们的群论分析表明，$Cmcm$结构与现有的拉曼和红外光谱数据兼容。至关重要的是，静态密度泛函理论计算显示$Cmcm$结构是玻恩-奥本海默势能面上的一个动力学不稳定鞍点，这证明对该问题进行完整的量子多体处理是必要的。这些结果为高压氢的相图提供了新的见解，并呼吁进一步的实验验证。