CAREER: Wave Mechanics of Complex, Correlated, and Driven Quantum Materials

该职业奖支持理论研究和教育，以促进对具有巨大技术前景的量子材料的理解。在这些化合物中，量子物理在实现特殊的电子或磁性能方面起着至关重要的作用。量子材料可以实现新的电子设备，可能基于高温超导性或拓扑鲁棒量子电路。超导体可以携带电流而不耗散，而拓扑状态是电子物质的新状态，可能使量子计算成为可能。实现这种潜力的一个障碍是这些系统经常表现出的复杂性。这个职业奖支持研究一个新的理论范式来解决这个问题，灵感来自所谓的多体定位。在量子物理学中，粒子可以表现得像波一样。多体定位是指量子波之间的干涉可以“冻结”相互作用电子的动力学，产生具有不同性质的不同类别的量子态。在这个项目中，局域化理论的思想将应用于许多相互作用电子的系统，并认为不同类型的激发态的统计分类对于确定复杂材料的性质可能是必不可少的。这与通常强调温度为绝对零度时基态性质的方法有很大不同。特别是，如果成功的话，这里开发的统计方法将提供新的理论工具来描述竞争电子相熔化产生的复杂行为。理解后者可能是释放量子材料技术应用潜力的关键。PI还将研究强电子-电子相互作用对量子材料中电荷和热量输运的作用。该项目的教育部分旨在通过强调算法和可视化，使现代数学工具更容易被本科物理专业的学生使用。在美国，物理学专业的学生目前学习的是20世纪以前发展起来的数学，但现在的研究使用了许多现代数学工具。这些可以用算法、解决问题的方法呈现给本科生。PI将创建学习模块，这些模块将在课堂上进行测试，并通过rice托管的永久网络存储库公开传播。该职业奖支持理论研究和教育，以促进对量子材料的理解。量子材料所展示的丰富多样的集体现象为技术带来了巨大的希望。实现这种潜力的一个障碍是这些系统经常表现出的复杂性。由于相互作用、挫折和材料无序的相互作用，许多化合物表现出竞争性的低温相。这些通常是在量子临界状态附近发现的，量子临界状态可能是由许多不同有序状态的波动引起的。现在认为，在无序或受挫的情况下，量子波干涉可以诱导多粒子相互作用系统的安德森局域化。这种多体定位表明了一种范式转移到多粒子状态的统计分类，而不是单一地关注基态。输运测量是量子干涉的主要探测，但理解相关材料中的输运仍然是一个挑战。项目目标包括：将在单体安德森局域物理中发展的统计方法应用于量子多粒子系统，揭示非费米液体中相关主导的输运效应。重点是低维量子临界状态和驱动拓扑系统。教育部分的目标是为物理和STEM学生和工作者提供更多的现代数学工具。具体的研究和教育目标是：1)验证多体局域化转变可以连续的假设，并研究预测在其上发生的“坏金属”相的物理性质。2)验证不同多体态概率峰之间的“聚类”决定坏金属相弛豫动力学的假设，研究不均匀性和单体态Chalker标度存在下的竞争顺序。3)通过利用二维拓扑绝缘体中边缘环阻力和量子猝灭动力学的新几何形状，以及通过强化相关电子流体热电输运中虚碰撞和实碰撞的作用，研究直接揭示相关性影响的新输运效应。4)开发和推广面向物理本科专业的现代数学主题虚拟学习模块，强调算法和可视化。PI将创建从李代数表示理论开始的学习模块，这些模块将在课堂上进行测试，并通过rice托管的永久网络存储库公开传播。从多体定位中产生的想法可能会导致对相关电子系统中竞争秩序、无序和挫折的相互作用的洞察；然而，关于多体定位转换的性质甚至存在的许多基本问题目前尚未得到解答，特别是在高于1的维度上。这些方法将(a)引入适用于精确数值或解析解的改进模型，以及(b)利用2D多体定位转变与特殊零度Anderson-Mott转变的接近性。竞争顺序和临界离域将研究在一个可积准晶体模型的相互作用版本。PI对热电输运的研究将与石墨烯方面的实验专家合作，并将帮助解开边缘费米液体中流体动力学、准粒子和输运寿命的作用。

NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education to advance understanding Quantum materials which hold great promise for technology. These are compounds in which quantum physics plays an essential role in enabling exceptional electronic or magnetic properties. Quantum materials may enable new electronic devices, perhaps based on high temperature superconductivity or topologically robust quantum circuits. Superconductors can carry electric current without dissipation while topological states are new states of electronic matter that may enable quantum computation. An obstacle to realizing this potential has been the complexity often exhibited by these systems. This CAREER award supports the investigation of a new theoretical paradigm to tackle this issue, inspired by so-called many-body localization. In quantum physics, particles can behave like waves. Many-body localization is the idea that the interference between quantum waves can "freeze" the dynamics of interacting electrons, producing different classes of quantum states with different properties. In this project, ideas from the theory of localization will be applied to systems of many interacting electrons, with the view that the statistical classification of different types of excited many-body states may prove essential for determining properties in complex materials. This is very different from the usual approaches that stress the properties of the ground state at the absolute zero of temperature. In particular, if successful, the statistical approach developed here will provide new theoretical tools to characterize the complex behavior that arises from the melting of competing electronic phases. Understanding the latter may be a key to unlocking the potential of quantum materials for technological applications. The PI will also investigate the role of strong electron-electron interactions on the transport of electric charge and heat in quantum materials. An educational component of the project aims to make modern mathematical tools more accessible to undergraduate physics majors by emphasizing algorithms and visualization. In the U.S., physics majors are currently taught mathematics developed prior to the 20th century, yet research now employs many more modern mathematical tools. These can be presented to undergraduates using an algorithmic, problem-solving, approach. The PI will create learning modules that will be tested in the classroom and openly disseminated via a permanent Rice-hosted web repository. TECHNICAL SUMMARYThis CAREER award supports theoretical research and education to advance understanding Quantum materials. The rich variety of collective phenomena exhibited by quantum materials holds great promise for technology. An obstacle to realizing this potential has been the complexity often exhibited by these systems. Due to the interplay of interactions, frustration, and material disorder, many compounds exhibit competing low temperature phases. These are often found in proximity to quantum critical regimes that may arise from fluctuations of the many different ordered states. It is now believed that quantum wave interference can induce the Anderson localization of a many-particle interacting system, in the presence of disorder or frustration. This many-body localization suggests a paradigm shift to the statistical classification of many-particle states, instead of a singular focus on the ground state. Transport measurements are the primary probe of quantum interference, but understanding transport in correlated materials remains a challenge. Project goals include: bringing statistical methods developed in one-body Anderson localization physics to bear on quantum many particle systems, and revealing correlation-dominated transport effects in non-Fermi liquids. The focus is on low-dimensional quantum critical regimes and driven topological systems. The goal of the educational component is to make available more modern mathematical tools to physics and STEM students and workers.Specific research and education objectives are to:1) Test the hypothesis that the many-body localization transition can be continuous, and investigate the physics of the "bad metal" phase predicted to occur above it.2) Test the hypothesis that "clustering" between the probability peaks of different many-body states determines the relaxation dynamics in the bad metal phase, and investigate competing orders in the presence of inhomogeneity and one-body state Chalker scaling.3) Investigate new transport effects that directly reveal the influence of correlations, by exploiting novel geometries for edge loop drag and quantum quench dynamics in 2D topological insulators, and by sharpening the roles of virtual and real collisions in the thermoelectric transport of correlated electron fluids.4) Develop and disseminate virtual learning modules for topics in modern mathematics accessible to undergraduate physics majors, emphasizing algorithms and visualization. The PI will create learning modules starting with Lie algebra representation theory, and these will be tested in the classroom and openly disseminated via a permanent Rice-hosted web repository.Ideas germinated from many-body localization may lead to insight into the interplay of competing orders, disorder, and frustration in correlated electron systems; however, many fundamental questions regarding the nature or even the existence of the many-body localization transition currently are unanswered, particularly in dimensions higher than one. The approaches will (a) introduce improved models amenable to exact numerical or analytical solutions, and (b) exploit the proximity of a 2D many-body localization transition to a special zero temperature Anderson-Mott transition. Competing orders and critical delocalization will be studied in an interacting version of an integrable quasicrystal model. The PI's investigation of thermoelectric transport will be in collaboration with experimentalists who are experts on graphene, and will help disentangle the roles of hydrodynamics, quasiparticle and transport lifetimes in marginal Fermi liquids.