含规范因子的神经网络量子蒙特卡洛方法用于磁场中的分子

中文摘要 AI 辅助

外磁场通过其与轨道和自旋运动的耦合，使关联电子态复杂化，并在波函数上施加依赖于坐标的相位，从而使得精确的电子结构计算变得更具挑战性。近年来，基于神经网络的量子蒙特卡洛（NNQMC）方法已成为研究磁场中无核系统的高精度方法。然而，对于分子系统，情况更为复杂，因为磁场会在远离规范原点的区域引入快速变化的相位。在此，我们引入一个含规范因子的相位因子，该因子直接作用于完整的多电子波函数，并考虑预设的磁场相位，留下一个更平滑的关联残差供网络学习。该因子极大地改善了分子平移一致性和大小一致性，为利用NNQMC研究磁场中的系统提供了一条途径。基于此方法，我们重现了H2中的弱场磁化率和强场键收缩。我们进一步将该方法应用于与白矮星相关的磁场下CN红色和C2 Swan系统中的选定跃迁。CN跃迁表现出比C2对应跃迁大得多的场致位移，表明其作为白矮星磁场探针的潜力。

英文摘要

External magnetic fields, through their coupling to orbital and spin motion, complicate the correlated electronic states and impose coordinate-dependent phases on the wavefunction, thereby making accurate electronic structure calculations substantially more demanding. Recently, neural network-based quantum Monte Carlo (NNQMC) has emerged as a highly accurate approach to study nucleus-free systems in magnetic fields. For molecular systems, however, things get more complicated as the magnetic field would introduce a rapidly varying phase in the region far from the gauge origin. Here we introduce a gauge-including phase factor that acts directly on the full many-electron wavefunction and accounts for the prescribed magnetic phase, leaving a smoother correlated residual for the network to learn. This factor greatly improves molecular translation consistency and size consistency, providing a route for studying systems in magnetic fields with NNQMC. Upon this approach, we reproduce weak-field magnetizabilities and strong-field bond contraction in \ce{H2}. We further apply the method to selected transitions in the \ce{CN} red and \ce{C2} Swan systems at magnetic fields relevant to white dwarfs. The \ce{CN} transition exhibits a much larger field-induced shift than its \ce{C2} counterpart, suggesting its potential as a probe of white-dwarf magnetic fields.

发表机构

• Fudan University（复旦大学）

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