用深度生成模型计算氢在温密物质区的物态方程，填补高温与低温方法间的空白。
Deep Variational Free Energy Calculation of Hydrogen Hugoniot
- 用三种深度生成模型联合优化变分自由能，模拟氢在高温下的电子与核行为。
- 在电子处于激发态的温密区域，获得高精度物态方程和热力学性质。
- 结果与实验和不同理论方法对比，可作为温密氢的重要基准参考。
我们构建了一种深度变分自由能框架，用于计算氢在温密物质区域的物态方程。该方法利用三种深度生成模型参数化有限温度下氢原子核与电子的变分密度矩阵：使用归一化流模型表示经典原子核的玻尔兹曼分布，自回归变换器模型描述激发态电子分布，以及对称等变流模型实现哈特里-福克态中电子坐标的幺正回流变换。通过联合优化这三个神经网络以最小化变分自由能，我们得到了电子处于激发态的温密氢的物态方程及相关的热力学性质。结果与氘的胡戈诺特曲线的其他理论与实验数据进行比较，旨在解决现有争议。我们的结果弥合了高温路径积分蒙特卡洛计算与低温基态电子方法之间的差距，为温密物质区氢提供了宝贵的基准数据。
原文摘要 · Abstract (English)
We develop a deep variational free energy framework to compute the equation of state of hydrogen in the warm dense matter region. This method parameterizes the variational density matrix of hydrogen nuclei and electrons at finite temperature using three deep generative models: a normalizing flow model for the Boltzmann distribution of the classical nuclei, an autoregressive transformer for the distribution of electrons in excited states, and a permutational equivariant flow model for the unitary backflow transformation of electron coordinates in Hartree-Fock states. By jointly optimizing the three neural networks to minimize the variational free energy, we obtain the equation of state and related thermodynamic properties of dense hydrogen for the temperature range where electrons occupy excited states. We compare our results with other theoretical and experimental results on the deuterium Hugoniot curve, aiming to resolve existing discrepancies. Our results bridge the gap between the results obtained by path-integral Monte Carlo calculations at high temperature and ground-state electronic methods at low temperature, thus providing a valuable benchmark for hydrogen in the warm dense matter region.
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