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

非技术性总结：量子材料代表了材料研究前沿的各种系统。这些材料拥有几种新颖且高度可调的物质状态，每种状态都具有跨不同科学和技术领域的变革潜力。然而，对这些系统进行建模是非常具有挑战性的，通常需要开发和使用先进的计算方法。该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，主要是出于各种技术原因。这一方面通常阻止了科学界获得这些相互作用如何影响不同材料性质的明确答案。PI的团队将利用新的模拟功能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。该团队还将提供各种光谱测量的预测，以指导未来对这些材料的实验。结合起来，该项目将有助于确定量子材料的组织原则，并促进其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，以加强科学工作者队伍。例如，PI的团队将开发新的培训材料和开源代码，用于执行量子材料的数值模拟，这些代码将与田纳西大学先进材料制造中心（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桥和核物理在田纳西州东部programmes.Technical摘要：了解强相关量子材料的属性是科学界面临的最前沿的挑战。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，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解决这个问题，以研究具有强e-ph相互作用的量子材料的广泛模型，利用PI小组开发的决定性量子蒙特卡罗（DQMC）算法的新开源实现。该代码可以模拟广泛的一类哈密顿算符，并使用混合蒙特卡罗方法来有效地对声子场进行采样，并克服通常与这些模拟相关的长自相关时间。PI和他的团队将使用这些功能来执行模型的数值精确模拟，这些模型超出了典型的Holstein模型，并对声子子系统进行了物理上真实的描述。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金属再到石墨烯衍生系统的材料的新兴特性。他们还将预测此类系统的光谱测量，以指导实验研究并对其结果进行关键验证。这个项目的一个特别的重点是广义苏-施里弗-希格类e-ph相互作用，其中原子运动耦合电子的动能通过调制的重叠积分。这种相互作用与新的现象有关，包括移动的（双）极化子，高温超导性，反铁磁性，新的电荷或键序，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，以加强科学工作者队伍。例如，PI的团队将开发新的培训材料和开源代码，用于执行量子材料的数值模拟，这些代码将与田纳西大学先进材料制造中心（NSF MRSEC中心）合作传播。最后，PI将继续现有的努力，通过与APS桥和核物理在田纳西州东部计划的合作伙伴关系，以增加在物理学中代表性不足的少数民族的机会。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.