Postdoc: Research Training for CS&E Postdoctoral Associate in Electronic Structure Theory

第一性原理电子结构计算已被证明是在微观尺度上研究物质性质的一种非常强大和准确的工具，它们扩展或补充了实验领域。它们的优势来自于无参数量子力学方法所固有的精确度和预测能力，来自它们在原子水平上提供的空间和时间描述的精细水平，以及最近强大计算资源的可获得性的扩展。然而，使用这些方法的传统实现来求解给定系统所需的时间与原子数量的三次方成正比，因此阻止了这种原本极其成功的方法扩展到大量感兴趣的系统。这一限制本质上是算法的；物理学及其相关的复杂性本质上与原子的数量成线性关系。该项目将实施和测试一种新的算法，该算法有望提供类似精度的计算方案，但只随系统规模线性扩展。该方案隐含地建立在单粒子密度矩阵的物理局域化基础上。这种相同的本地化特性使得这样的算法非常适合在大规模并行计算机体系结构上实现。

First-principle electronic structure calculations have proven to be a very powerful and accurate tool for investigating the properties of matter at microscopic scales, where they extend or complement the domain of experiments. Their strength comes from the precision and predictive power that is inherent in a parameter-free quantum-mechanical approach, from the fine level of detail of the spatial and temporal description they provide at the atomic level, and from the recent expansion in the availability of powerful computational resources. However, the time needed to solve a given system using conventional implementations of these methods is proportional to the third power of the number of atoms, thus preventing the extension of this otherwise extremely successful approach to a great many systems of interest. This limitation is algorithmic in nature; the physics and its associated complexity inherently scale linearly with the number of atoms. The project will implement and test a new algorithm which holds the promise of providing a computational scheme of comparable accuracy, but which scales only linearly with system size. This scheme is built implicitly on the physical localization of the one-particle density matrix. This same localizational property makes such an algorithm highly appropriate for implementation on a massively parallel computer architecture.