Collaborative Research: Worm Algorithm and Diagrammatic Monte Carlo for strongly correlated condensed matter systems

该奖项支持对材料中电子和固体氦-4的集体量子力学行为的合作研究和教育。该项目正在使用并进一步开发两种最先进的计算方法，适用于研究由许多相互作用粒子组成的量子力学系统，即蠕虫算法（WA）和Diagrammatic Monte Carlo（DiagMC），这两种方法都是由研究团队引入的。通过WA，该团队希望进一步了解氦-4的不完美晶体在接近绝对零度的低温下所表现出的惊人特性，例如氦-4原子通过晶体的无摩擦传输，称为超传输，以及对任意弱应力的几乎类似液体的响应，称为量子塑性。通过DiagMC，该团队将解决一些关于多电子系统行为的众所周知的难题，包括电子如何发展合作量子力学状态成为超导体的问题。超导体可以在没有电阻的情况下导电。理解固态氦-4中的量子塑性、超输运以及它们之间的相互作用是现代低温物理学的一个重大挑战。更一般地说，迫切需要适用于描述物理学，量子化学和材料科学所有领域的电子集体量子行为的通用方法。该项目的核心模拟提供了有关这些系统的定量和定性性质的关键信息，测试分析预测，帮助建立适当的理论框架，并为实验数据的明确分析和测量技术的进一步发展提供基础。该项目的一个组成部分是对研究生进行先进理论和数值技术的培训，以及并行计算。该项目涉及开发和维护一个关于所使用的数值方法的教程网站，PI计划编辑一本针对广泛科学受众的书籍。该奖项支持关于材料中电子和固体氦-4的集体量子行为的合作研究和教育。PI将使用并进一步开发研究团队引入的两种最先进的Monte Carlo方法：蠕虫算法（WA）和Diagrammatic Monte Carlo（DiagMC）。该项目的主要目标是：i）使用DiagMC来研究众所周知的困难凝聚态问题，例如：费米子排斥哈伯德模型中的库珀不稳定性，包括高临界温度的可能性，用长程库仑和电子-声子相互作用的受控从头计算处理来模拟电子系统，为强相关模型创建替代公式，理解受抑自旋模型中量子与经典的对应关系; ii）开展固体He-4中无序诱导量子物理的WA研究，例如与一般（倾斜）位错相关的超输运和量子可塑性。了解量子可塑性、超输运，在固态氦-4中，它们之间的相互作用是现代低温物理学的一个重大挑战。更普遍地说，迫切需要适用于物理学、量子化学和材料科学所有领域的强关联费米子系统的通用方法。该项目的核心模拟提供了有关这些系统的定量和定性性质的关键信息，测试分析预测，帮助建立适当的理论框架，并为实验数据的明确分析和测量技术的进一步发展提供基础。该项目的一个组成部分是对研究生进行先进理论和数值技术的培训，以及并行计算。该项目涉及开发和维护一个关于所使用的数值方法的教程网站，PI计划编辑一本针对广泛科学受众的书籍。

NONTECHNICAL SUMMARYThis award supports collaborative research and education on the collective quantum mechanical behavior of electrons in materials and of solid helium-4. The project is using and further developing two state-of-the-art computational approaches suitable for the study of quantum mechanical systems consisting of many interacting particles, the Worm Algorithm (WA) and Diagrammatic Monte Carlo (DiagMC), which were both introduced by the research team. With WA the team expects to advance understanding of striking properties demonstrated by imperfect crystals of helium-4 at low temperatures near the absolute zero of temperature, such as the frictionless transport of helium-4 atoms through the crystal, called supertransport, and an almost liquid-like response to an arbitrarily weak stress, called quantum plasticity. With DiagMC the team will address certain notoriously difficult problems concerning the behavior of many-electron systems, including the problem of how electrons develop the cooperative quantum mechanical state to become superconductors. Superconductors can conduct electricity without resistance.Understanding quantum plasticity, supertransport, and the interplay between them in solid helium-4 is a major challenge for modern low-temperature physics. More generally, there is an urgent need for universal methods suitable for describing the collective quantum behavior of electrons across all fields of physics, quantum chemistry, and materials science. The simulations at the core of the project provide crucial information about quantitative and qualitative properties of these systems, test analytical predictions, help establish the proper theoretical framework, and provide foundation for the unambiguous analysis of experimental data and the further development of measuring techniques.An integral part of the project is the training of graduate students in advanced theoretical and numerical techniques, as well as in parallel computing. The project involves developing and maintaining a tutorial website on the numerical methods used, and the PIs plan to edit a book on the same, targeting a broad scientific audience. TECHNICAL SUMMARYThis award supports collaborative research and education on the collective quantum behavior of electrons in materials and of solid helium-4. The PIs will use and further develop two state-of-the-art Monte Carlo methods introduced by the research team: the Worm Algorithm (WA), and Diagrammatic Monte Carlo (DiagMC). The main goals of the project are: i) to use DiagMC for studying notoriously difficult condensed-matter problems such as: the Cooper instability in the fermionic repulsive Hubbard model including the possibility of high critical temperatures, modeling electronic systems with controlled ab initio treatment of long-range Coulomb and electron-phonon interactions, creating alternative formulations for strongly correlated models, and understanding the quantum-to-classical correspondence in frustrated spin models; ii) to carry out WA studies of disorder-induced quantum physics in solid He-4, such as supertransport and quantum plasticity associated with generic (tilted) dislocations.Understanding quantum plasticity, supertransport, and the interplay between them in solid helium-4 is a major challenge for modern low-temperature physics. More generally, there is an urgent need for universal methods suitable for strongly correlated fermionic systems across all fields of physics, quantum chemistry, and materials science. The simulations at the core of the project provide crucial information about quantitative and qualitative properties of these systems, test analytical predictions, help establish the proper theoretical framework, and provide foundation for the unambiguous analysis of experimental data and the further development of measuring techniques.An integral part of the project is the training of graduate students in advanced theoretical and numerical techniques, as well as in parallel computing. The project involves developing and maintaining a tutorial website on the numerical methods used, and the PIs plan to edit a book on the same, targeting a broad scientific audience.