CDS&E: Quantum Monte Carlo Methods for Electron Correlations and Spin-Orbit Effects in Low-Dimensional Materials

非技术总结该奖项支持对相互作用量子系统的性质和行为的理论和计算研究。这是当前凝聚态物质和材料物理学最具影响力的前沿领域之一。特别是，具有纳米量级(十亿分之一米大小)的低维结构，以及电子与其空间和自旋自由度之间的各种竞争相互作用，为开发具有超低功耗和超快处理速度的新材料和设备提供了前所未有的新机遇。阻碍这一潜力实现的关键障碍是我们对如何有效和准确地描述、修改和控制相关量子机制的有限知识。PI和他的团队将专注于求解基本方程的高性能计算方法，并建立一套新的工具，用于分析量子现象和发现由纳米组件组成的新材料。该方法基于复杂的解析结构、稳健有效的模拟方法和大型并行计算平台的高性能的优化组合。计算开发将成为开放源码模拟包的一部分，供广大研究社区使用。这项工作的固有部分将是对研究生进行先进模拟方法和纳米系统物理方面的培训。这种培训预计将为未来的科学研究职业生涯提供多种机会。通过扩展北卡罗来纳州立大学的课程，这项研究的教育影响将进一步增强，开发一门计算物理研究生课程，重点是量子系统的模拟和相关主题，涉及物理、化学、材料和工程学科的广泛兴趣。该奖项支持专注于为低维材料研究开发计算量子蒙特卡罗方法的计算和理论研究。首先，基于对密度矩阵显式包含配对效应的有效哈密顿量，将建立构造多体配对波函数的新方法。这将以一种稳健和系统的方式为相关的试波函数构造提供关键输入，以便在不同的自旋极化和对称性上一致地描述电子关联。因此，与主流的电子结构方法相比，结合能、离解能、自旋能隙和激发态等重要物理量的量子蒙特卡罗方法的计算精度将显著提高。第二，将自旋视为真正的量子变量的量子蒙特卡罗方法将被开发和实施，用于具有重要自旋相互作用的系统的常规计算。这一发展将在电子结构计算方面开辟新的天地，并将使在多体波函数环境下研究具有显著自旋-轨道效应的材料和具有非共线自旋或拓扑有序态的系统成为可能。计划中的应用和原型瞄准了低维和自旋电子纳米材料(如掺杂石墨烯和相关系统)的前景广阔的研究挑战。计算开发将成为开放源码模拟包的一部分，供广大研究社区使用。这项工作的固有部分将是对研究生进行先进模拟方法和纳米系统物理方面的培训。这种培训预计将为未来的科学研究职业生涯提供多种机会。这项研究的教育影响将通过扩展北卡罗来纳州立大学的课程进一步加强，开发一门计算物理研究生课程，重点是量子系统的模拟和相关主题，涉及物理、化学、材料和工程学科的广泛兴趣。

NON-TECHNICAL SUMMARYThis award supports theoretical and computational research on properties and behavior of interacting quantum systems. This is one of the most impactful frontiers of current condensed matter and materials physics. In particular, low-dimensional structures with sizes of the order of a nanometer (one billionth the size of a meter) with various competing interactions between the electrons and their spatial and spin degrees of freedom offer new and unprecedented opportunities for the development of new materials and devices with ultralow power consumption and ultrafast processing speeds. The key barrier that hampers the realization of this potential is our limited knowledge of how to efficiently and accurately describe, modify and control the relevant quantum mechanisms. The PI and his group will focus on high-performance computational approaches for solving the underlying fundamental equations and establish a new set of tools for analysis of quantum phenomena and for discovery of new materials made up of nanometer-sized components. The proposed methodology is based on an optimized combination of sophisticated analytical constructions, robust and effective simulation approaches, and high performance of large parallel computing platforms. The computational developments will become a part of an open source simulation package for use by research communities at large. Inherent part of the effort will be the training of a graduate student in advanced simulation methods and the physics of nanometer-sized systems. Such training is expected to provide multiple opportunities for a future career in scientific research. The educational impact of this research will be further enhanced through expansion of the curriculum at North Carolina State University by developing a graduate computational physics course with emphasis on simulations of quantum systems and related topics with broad interest across physics, chemistry, materials and engineering disciplines.TECHNICAL SUMMARY This award supports computational and theoretical research focused on the development of computational quantum Monte Carlo methods for studies of low-dimensional materials. First, novel approaches for constructions of many-body pairing wave functions will be established using effective Hamiltonians with explicit inclusion of pairing effects based on pair density matrices. This will provide the key inputs for correlated trial wave function constructions in a robust and systematic manner so that electron correlations will be described consistently across varying spin-polarizations and symmetries. As a result, the quantum Monte Carlo accuracy for important quantities such as binding and dissociation energies, spin gaps, and excitations will increase very significantly when compared with mainstream electronic structure approaches. Second, quantum Monte Carlo methods for treating spins as genuine quantum variables will be developed and implemented for routine use in calculations of systems with important spin interactions. This development will break new ground in electronic structure calculations and will make studies of materials with significant spin-orbit effects and systems with non-collinear spins or topologically ordered states possible in a many-body wave function setting. The planned applications and prototypes target promising research challenges in low-dimensional and spintronic nanomaterials such as doped graphene and related systems. The computational developments will become a part of an open source simulation package for use by research communities at large. Inherent part of the effort will be the training of a graduate student in advanced simulation methods and the physics of nanometer-sized systems. Such training is expected to provide multiple opportunities for a future career in scientific research. The educational impact of this research will be further enhanced through expansion of the curriculum at North Carolina State University by developing a graduate computational physics course with emphasis on simulations of quantum systems and related topics with broad interest across physics, chemistry, materials and engineering disciplines.