Postdoc: Algorithm for Treating Correlated Many-Fermion Systems on a Lattice, the Constrained Path Monte-Carlo (CPMC) Method

这个项目将解决计算物理中的一个核心算法问题，即对服从费米子统计的强相互作用量子力学系统进行可靠的计算。这类系统的一些例子包括高温超导体、重费米子金属和磁性材料。挑战在于正确和准确地处理微观相关性，这对于理解这些系统的特性及其理论和技术影响至关重要。该项目将基于最近开发的一种处理格子上的关联多费米子系统的算法，即约束路径蒙特卡罗(CPMC)方法。它由三个独立但密切相关的部分组成：(1)用于电子关联的原型格子模型的基态性质；(2)有限温度；(3)连续统系统。所有这些都将在可伸缩并行计算算法的背景下完成，这是研究与高温超导体和重费米子材料密切相关的晶格模型问题的关键方面。新版本的CPMC算法将被开发用于有限温度计算。这将使热力学性质的研究和真正的相变成为可能。该项目还将算法扩展到连续体，从而实现更逼真的材质计算。

This project will address a central algorithmic problem in computational physics, namely, reliable calculations for strongly interacting quantum mechanical systems that obey fermion statistics. Some examples of such systems include high-temperature superconductors, heavy-fermion metals, and magnetic materials. The challenge lies in the correct and accurate treatment of microscopic correlations, which is essential to understanding the properties of these systems and their theoretical and technological implications. The project will be based on a recently developed algorithm for treating correlated many-fermion systems on a lattice, the Constrained Path Monte Carlo (CPMC) Method. It consists of three separate but closely related parts: (1) The Ground-State Properties of Prototypical Lattice models for Electron Correlation; (2) Finite Temperature; (3) Continuum Systems. All of this will be done in the context of scaleable parallel computing algorithms, a critical aspect of the problem of studying lattice models of great relevance to high-temperature superconductors and heavy-fermion materials. A new version of the CPMC algorithms will be developed for finite temperature calculations. This will enable studies of thermodynamically properties and true phase transitions. This project will also extend the algorithm to the continuum, which will enable more realistic calculations of materials.