Disorder and dynamics in quantum materials

非技术总结该奖项支持有关材料在低温下的量子性质的理论和计算研究和教育。在接近绝对零度的温度下，材料的行为通常受量子力学的支配。这个项目的目标是探索杂质如何影响材料的量子态，即天然或人造材料中永远无法完全避免的缺陷和其他类型的缺陷。具体地说，这项研究的目的是了解杂质和缺陷如何影响物质的不同量子相之间的相互作用和/或竞争，即不同类型的量子态，如超导和磁性，以及这些不同相之间的转换，称为量子相变。此外，这些活动将向本科生和研究生以及职业生涯早期的科学家介绍尖端材料研究，通过一个可公开访问的网页改进计算教育和研究基础设施，该网页介绍如何建立和维护用于科学计算的计算机集群，并通过每年一次的“诺贝尔奖讨论会”传达科学发现的兴奋，该讨论会提供对奖项背后的科学的基本介绍。技术总结该奖项支持低温下量子材料性质的理论和计算研究和教育。科学目标是：i)了解接近无序量子相变的系统的动力学，以及ii)探索随机性对具有复杂交织有序的材料的影响。无序量子多粒子系统的动力学目前引起了极大的关注，从统计物理的基础一直到传输新的量子材料和器件的实验。本项目研究无序量子相变附近的实时动力学和输运性质，特别关注集体模及其局域和标度性质。最初，重点将放在无序玻色子的莫特玻璃相和玻色玻璃相上，后来的研究将扩大到无限随机相和跃迁。量子材料通常具有几种不同类型的有序，这些有序似乎交织在其复杂相图的大范围内。杂质和缺陷以不同的方式耦合到不同类型的有序，因此它们可以部分熔化复杂的有序参数，并稳定新的物质相。本课题系统地研究了随机性对系统相图和相变的影响。主要研究人员采用分析和计算相结合的方法进行这项研究，包括重整化群计算、渗流理论、大规模蒙特卡罗模拟、精确对角化和量子平均场理论。此外，这些活动将通过以下方式对社会产生更广泛的影响：1)培养学生和职业生涯早期的科学家；2)向不同的受众传播科学发现的兴奋；以及iii)通过可公开访问的网页改进PI机构及其他机构的计算研究和教育基础设施，该网页包含如何构建和维护用于科学计算的计算机集群的说明。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports theoretical and computational research and education into the quantum properties of materials at low temperatures. Close to the absolute zero of temperature, the behavior of materials is usually governed by quantum mechanics. The goal of this project is to explore how the quantum state of a material is affected by impurities, i.e. defects and other types of imperfections that can never be completely avoided in either natural or man-made materials. Specifically, the research aims at understanding how impurities and defects influence the interplay and/or competition between different quantum phases of matter, that is, different types of quantum states such as superconductivity and magnetism, as well as the transformations, called quantum phase transitions, between these different phases. In addition, the activities will introduce undergraduate and graduate students as well as early-career scientists to cutting-edge materials research, improve computational education and research infrastructure via a publicly accessible web page with instructions on how to build and maintain a computer cluster for scientific calculations, and communicate the excitement of scientific discovery by means of yearly "Nobel Prize Colloquia" that provide elementary introductions into the science behind the prizes.TECHNICAL SUMMARYThis award supports theoretical and computational research and education into the properties of quantum materials at low temperatures. The scientific objectives are: i) to understand the dynamics of systems close to disordered quantum phase transitions, and ii) to explore the effects of randomness on materials featuring complex intertwined orders.The dynamics of disordered quantum many-particle systems is currently attracting enormous attention with questions ranging from the very foundations of statistical physics all the way to transport experiments in novel quantum materials and devices. This project studies the real-time dynamics and transport properties close to disordered quantum phase transitions, paying particular attention to collective modes and their localization and scaling properties. Initially, the focus will be on the Mott glass and Bose glass phases of disordered bosons, while later the research will broaden to infinite-randomness phases and transitions.Quantum materials often feature several different kinds of orders that appear to be intertwined over large regions of their complex phase diagrams. Impurities and defects couple differently to different types of order, they can therefore partially melt a complex order parameter and stabilize novel phases of matter. This project studies systematically the effects of randomness on the phase diagram and the phase transitions in such systems. Examples include the nematicity arising from spin- and charge-density-wave orders as well as the intertwining of magnetic and ferroelectric orders in hexaferrites.The principal investigator employs a combination of analytical and computational methods to perform this research including renormalization group calculations, percolation theory, large-scale Monte-Carlo simulations, exact diagonalization, and quantum mean-field theories.In addition, the activities will impart broader impacts on society by i) training students and early-career scientists, ii) communicating the excitement of scientific discovery to diverse audiences, and iii) improving the computational research and education infrastructure at the PI's institution and beyond via a publicly accessible web page with instructions on how to build and maintain a computer cluster for scientific calculations.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.