Non-perturbative studies of electron-lattice interactions in quantum materials

非技术总结：量子材料代表了材料研究前沿的不同类别的系统。这些材料拥有几种新颖且高度可调的物质状态，每种状态在不同的科学和技术领域都具有变革潜力。然而，对这些系统进行建模是非常具有挑战性的，并且通常需要开发和使用先进的计算方法。这个项目的重点是对量子材料进行最先进的数值模拟，其中电子与原子的运动强烈相互作用。虽然这些相互作用被认为在不同的量子材料家族中起着关键作用，但以前的数值研究往往集中在过于简化的模型上，主要是由于各种技术原因，这些模型具有不切实际的参数。这方面通常阻碍了科学界对这些相互作用如何影响不同材料的性质获得明确的答案。PI的团队将利用新的模拟能力对不同的量子材料进行详细的模拟，同时包括对形成材料的电子和原子晶格之间相互作用的真实描述。该团队还将为各种光谱测量提供预测，以指导未来对这些材料的实验。结合起来，这个项目将有助于确定量子材料的组织原理，并促进它们在未来科学和技术应用中的使用。该项目还将扩大对计算科学的参与，并提供尖端计算方法的培训，以增强科学劳动力。例如，PI的团队将开发新的训练材料和开源代码，用于执行量子材料的数值模拟，这将与田纳西大学的先进材料和制造中心（NSF MRSEC中心）合作传播。最后，PI将继续现有的努力，旨在通过与APS桥梁和田纳西州东部核物理项目的合作，增加未被充分代表的少数民族在物理学方面的机会。技术总结：了解强相关量子材料的性质是科学界面临的一个前沿挑战。这些材料通常具有很强的电子-电子和电子-声子（e-ph）相互作用，产生相关的电子液体，这违背了基于单粒子理论的理论描述。模拟它们的行为通常需要非微扰数值方法；然而，解决现实的e-ph相互作用仍然是一个关键的挑战。该项目通过应用最先进的量子蒙特卡罗方法来研究承载强e-ph相互作用的量子材料的广泛类别模型，利用PI小组开发的新的决定量子蒙特卡罗（DQMC）算法的开源实现，解决了这个问题。该代码可以模拟广泛的哈密顿量，并使用混合蒙特卡罗方法有效地对声子场进行采样，并克服了与这些模拟通常相关的长自相关时间。PI和他的团队将利用这些能力，在标准霍尔斯坦模型之外，对声子子系统进行物理上真实的描述，对模型进行精确的数值模拟。具体来说，他们将研究e-ph耦合如何影响从非常规超导体到kagome金属到石墨烯衍生系统等材料的涌现特性。他们还将预测这些系统的光谱测量，以指导实验研究，并为其结果提供关键的验证。这个项目特别关注的是广义的Su-Schrieffer-Heeger-like e-ph相互作用，其中原子运动通过重叠积分的调制耦合电子的动能。这种相互作用与各种新现象有关，包括移动极化子、高温超导、反铁磁性、新电荷或键序以及物质的拓扑状态。该项目还将扩大对计算科学的参与，并提供尖端计算方法的培训，以增强科学劳动力。例如，PI的团队将开发新的训练材料和开源代码，用于执行量子材料的数值模拟，这将与田纳西大学的先进材料和制造中心（NSF MRSEC中心）合作传播。最后，PI将继续现有的努力，通过与APS桥梁和田纳西州东部核物理项目的合作，增加未被充分代表的少数民族在物理学方面的机会。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Nontechnical Summary:Quantum materials represent a diverse class of systems at the forefront of materials research. These materials host several novel and highly tunable states of matter, each with transformative potential across different science and technology sectors. Modeling these systems is incredibly challenging, however, and often requires the development and use of advanced computational methods. This project focuses on performing state-of-the-art numerical simulations of quantum materials where the electrons interact strongly with the motion of the atoms. While these interactions are believed to play a key role in different families of quantum materials, previous numerical studies have often concentrated on oversimplified models with unrealistic parameters primarily for various technical reasons. This aspect has generally prevented the scientific community from obtaining definitive answers to how these interactions influence the properties of different materials. The PI’s team will leverage new simulation capabilities to perform detailed simulations of different quantum materials while including realistic descriptions of the interactions between the electrons and lattice of atoms that form the material. The team will also provide predictions for various spectroscopic measurements to guide future experiments on these materials. Combined, this project will help identify organizing principles for quantum materials and facilitate their use in future scientific and technological applications. This project will also broaden participation in computational science and provide training in cutting-edge computational methods to enhance the scientific workforce. For example, the PI’s team will develop new training materials and open-source codes for performing numerical simulations of quantum materials, which will be disseminated in partnership with the University of Tennessee’s Center for Advanced Materials & Manufacturing, an NSF MRSEC center. Finally, the PI will continue existing efforts aimed at increasing opportunities for underrepresented minorities in physics through partnerships with the APS Bridge and Nuclear Physics in Eastern Tennessee programs.Technical Summary:Understanding the properties of strongly correlated quantum materials is a forefront challenge for the scientific community. These materials often host strong electron-electron and electron-phonon (e-ph) interactions, which produce correlated electron liquids that defy theoretical descriptions based on single-particle theories. Modeling their behavior often requires nonperturbative numerical methods; however, addressing realistic e-ph interactions remains as a key challenge. This project addresses this problem by applying state-of-the-art quantum Monte Carlo methods to study broad classes of models for quantum materials hosting strong e-ph interactions, leveraging a new open-source implementation of the determinant quantum Monte Carlo (DQMC) algorithm developed by the PI’s group. This code can simulate a broad class of Hamiltonians and uses hybrid Monte Carlo methods to sample the phonon fields efficiently and overcome the long autocorrelation times typically associated with these simulations. The PI and his team will use these capabilities to perform numerically exact simulations of models beyond the canonical Holstein model with physically realistic descriptions of the phonon subsystem. Specifically, they will study how the e-ph coupling influences the emergent properties of materials ranging from unconventional superconductors to kagome metals to graphene-derived systems. They will also predict spectroscopic measurements on such systems to guide experimental studies and provide crucial validation of their results. A particular focus for this project is on generalized Su-Schrieffer-Heeger-like e-ph interactions, where the atomic motion couples the electron’s kinetic energy via a modulation of the overlap integral. This interaction has been linked to novel phenomena ranging from mobile (bi)polarons, high-temperature superconductivity, antiferromagnetism, novel charge or bond orders, and topological states of matter. This project will also broaden participation in computational science and provide training in cutting-edge computational methods to enhance the scientific workforce. For example, the PI’s team will develop new training materials and open-source codes for performing numerical simulations of quantum materials, which will be disseminated in partnership with the University of Tennessee’s Center for Advanced Materials & Manufacturing, an NSF MRSEC center. Finally, the PI will continue existing efforts to increase opportunities for underrepresented minorities in physics through partnerships with the APS Bridge and Nuclear Physics in Eastern Tennessee programs.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.