标题： 高压氢的通用神经波函数 显示英文标题

标题： Universal neural wave functions for high-pressure hydrogen

摘要： 我们利用神经量子态的力量来描述固态和液态致密氢的基态波函数，包括电子和质子自由度。 对于静止质子，所得的Born-Oppenheimer能量始终低于所有之前针对包含最多$128$个氢原子系统的投影蒙特卡洛计算。 与传统方法不同，我们引入了一个通用的试探波函数，其变分参数在覆盖广泛压强-温度范围且涵盖分子相和原子相的一组大质子构型上同时优化。 这种全局优化不仅相比基准测试获得了更低的能量，还大大降低了计算成本。 通过在零温基态中包含核量子效应，从而超越Born-Oppenheimer近似，我们的描述克服了当前波函数的主要局限性，特别是通过避免对预期量子晶体的显式对称性假设，并绕过了不同质量尺度下虚时演化的效率问题。 作为首次应用，我们研究了一个极高密度区域中的晶体形成，该区域预计会发生压力诱导的熔化。 显示英文摘要

摘要： We leverage the power of neural quantum states to describe the ground state wave function of solid and liquid dense hydrogen, including both electronic and protonic degrees of freedom. For static protons, the resulting Born-Oppenheimer energies are consistently lower than all previous projector Monte Carlo calculations for systems containing up to $128$ hydrogen atoms. In contrast to conventional methods, we introduce a universal trial wave function whose variational parameters are optimized simultaneously over a large set of proton configurations spanning a wide pressure-temperature spectrum and covering both molecular and atomic phases. This global optimization not only yields lower energies compared to benchmarks but also brings an enormous reduction in computational cost. By including nuclear quantum effects in the zero-temperature ground state, thus going beyond the Born-Oppenheimer approximation, our description overcomes major limitations of current wave functions, notably by avoiding any explicit symmetry assumption on the expected quantum crystal and sidestepping efficiency issues of imaginary time evolution with disparate mass scales. As a first application, we examine crystal formation in an extremely high-density region where pressure-induced melting is expected.