CMG COLLABORATIVE RESEARCH: Quantum Monte Carlo Calculations of Deep Earth Materials

量子蒙特卡罗是研究物理和化学中真实材料的最精确的模拟技术之一，与传统的密度泛函理论相比，它在精度上有了显著的提高。目前S QMC方法的一个重要局限性就是计算要求很高。由于QMC计算的很大一部分花费在形成和评估斯莱特行列式上，该团队计划开发不同的局部化变换，以获得稀疏行列式。稀疏性可以在多层预处理器、不完全分解预处理器和迭代求解器中得到利用，以达到随系统大小的线性缩放。新开发的QMC方法将使该团队能够获得地球物理学高度感兴趣的固体材料的精确状态方程、相变和弹性。我们将使用QMC来确定铁在镁铁矿、钙钛矿和后钙钛矿(Mg，Fe)SiO_3固溶体中的自旋状态以及水-二氧化碳混合物的性质。我们对地球内部的了解来自地震观测和高压地质物质的表征。这种表征不仅是通过高压实验室实验获得的，也是通过计算机模拟获得的，因为材料的性质取决于原子之间的相互作用，而这些相互作用可以通过计算机模拟从物理基本定律中确定。本项目致力于通过发展新的数学技术来改进量子蒙特卡罗方法，使这些模拟方法更加准确。这些新开发的方法将使该团队能够在高压下表征不同的金属氧化物、硅酸盐以及液态水和二氧化碳的混合物。

Quantum Monte Carlo is among the most precise simulation techniques to study realistic materials in physics and chemistry and provides a significant gain in precision compared with traditional density functional theory. One significant limitation of today?s QMC methods is the high computational demand. Since a substantial part of the QMC computation is spent in on forming and evaluating Slater determinants, the team plans to develop different localization transformations in order to obtain sparse determinants. The sparsity can be exploited in multilevel preconditioners, incomplete decomposition preconditioners, and iterative solvers to reach linear scaling with system size. The newly developed QMC methods will enable the team to obtain accurate equations of state, phase transitions, and elasticity of solid materials that are of high interest in geophysics. The spin state of iron in solid solutions magnesiowustite, perovskite and post-perovskite (Mg,Fe)SiO3 as well as the properties of water-carbon dioxide mixtures will be determined using QMC.Our understanding of the interior of the Earth comes from seismic observations and from the characterization of geological materials at high pressure. This characterization is not only obtained with high-pressure laboratory experiments but also with computer simulations because the properties of materials depend on the interactions between the atoms and those can be determined with computer simulations from the fundamental laws of physics. This project focuses on making those simulation methods much more accurate by developing new mathematical techniques to improve the quantum Monte Carlo method. These newly developed methods will enable the team to characterize different metal oxides, silicates, and mixtures of fluid water and carbon dioxide at high pressure.