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

该奖项支持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中最具影响力的前沿之一。特别是，具有纳米量级（一米大小的十亿分之一）尺寸的低维结构，具有电子及其空间自由度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器件提供了新的和前所未有的机会。阻碍实现这一潜力的关键障碍是我们对如何有效、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解决潜在基本方程的高性能计算方法，并建立一套新的工具来分析量子现象和发现由纳米级组件组成的新材料。所提出的方法是基于复杂的分析结构、鲁棒有效的仿真方法和高性能的大型并行计算平台的优化组合。计算的发展将成为开源模拟包的一部分，供研究团体广泛使用。这项工作的固有部分将是训练研究生掌握先进的模拟方法和纳米系统的物理学。这样的培训有望为未来的科研事业提供多种机会。这项研究的教育影响将通过扩展北卡罗莱纳州立大学的课程来进一步增强，通过开发研究生计算物理课程，重点是量子系统的模拟和相关主题，在物理，化学，材料和工程学科中具有广泛的兴趣。该奖项支持专注于开发用于低维材料研究的计算量子蒙特卡罗方法的计算和理论研究。首先，利用有效哈密顿量建立多体配对波函数的新构造方法，并明确包含基于对密度矩阵的配对效应。这将以稳健和系统的方式为相关试波函数结构提供关键输入，以便在不同的自旋极化和对称性中一致地描述电子相关性。因此，与主流电子结构方法相比，对结合能和离解能、自旋间隙和激发等重要量的量子蒙特卡罗精度将大大提高。其次，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现，用于计算具有重要自旋相互作用的系统的常规使用。这一发展将在电子结构计算方面开辟新的领域，并将使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在多体波函数设置中成为可能。计划中的应用和原型针对低维和自旋电子纳米材料（如掺杂石墨烯和相关系统）的有前途的研究挑战。计算的发展将成为开源模拟包的一部分，供研究团体广泛使用。这项工作的固有部分将是训练研究生掌握先进的模拟方法和纳米系统的物理学。这样的培训有望为未来的科研事业提供多种机会。这项研究的教育影响将通过扩展北卡罗莱纳州立大学的课程来进一步增强，通过开发研究生计算物理课程，重点是量子系统的模拟和相关主题，在物理，化学，材料和工程学科中具有广泛的兴趣。

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.