RUI: Disorder in Strongly-Correlated Electrons on a Lattice

RUI：晶格上强相关电子的无序

• 批准号: 1609560
• 负责人: Ehsan Khatami
• 金额: $ 17.1万
• 依托单位: San Jose State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-12-01 至 2019-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1609560&HistoricalAwards=false
• 关键词: RUI; Disorder; Strongly; Correlated; Electrons

NONTECHNICAL SUMMARYThis award supports theoretical research and education in the physics of disorder and its effect on how electrons organize in real materials. Theoretical study and understanding of fundamental properties of solids that exhibit unexpected and often technologically useful properties at low temperatures commonly rely on the assumption that atoms form perfectly periodic lattices. However, disorder (crystal defects or impurities) that exists in real materials cannot always be ignored when studying electronic properties. Together with all the other important players in the system (crystal lattice geometry, interaction between electrons, etc.), their presence can drive the system as a whole to phases that do not appear if one considers disorder alone, or only electronic interactions. The accurate description of such an inclusive system using current numerical techniques can be a daunting task. In this project, the PI will implement a novel idea for efficiently taking random disorder into account in certain numerical simulations of interacting electrons. The PI will use the method to study the collective rearrangements of electrons and the different transformations they can undergo. The results will help interpret experimental observations, and will ultimately help understand the mechanism behind the creation of exotic phases, such as insulating and superconducting phases, with possible applications in the technology and energy sectors. The activities will provide several undergraduate students from the diverse population of San Jose State University with hands-on research experience in the field of computational condensed matter physics, and with opportunities to improve their scientific communication skills through writing papers and presenting their findings at national scientific meetings. The award also supports the PI in his efforts to integrate research and undergraduate education through the incorporation of computational methods into physics courses. TECHNICAL SUMMARYThis award supports theoretical research and education in the physics of disorder and its effect on electronic phase transitions. The interplay of disorder, caused by impurities or crystal defects in real materials, and electronic correlations in condensed matter physics is only poorly understood. Important questions about the effect of disorder on the appearance and nature of phase transitions, as well as on the fate of the Anderson localization upon introduction of electronic interactions in different dimensions, remain largely unsettled. This is especially true for fermionic systems and the corresponding quantum lattice models that emulate disorder effects through random-site or bond energies. Recent experiments with ultracold Fermi gasses on optical lattices have begun to shed light on some of these questions. However, much like in experimental simulations with clean lattices, these experiments rely on approximation-free and highly precise numerical simulations for thermometry and characterization. In this project the PI will implement a new idea for the treatment of continuous random disorder in the numerical linked-cluster expansion, an emerging and powerful method that yields exact finite-temperature results for strongly correlated electronic systems in the thermodynamic limit. Using this method, the PI will study the thermodynamic properties, including various magnetic and/or superconducting correlations of Heisenberg and Hubbard models in two and three dimensions. The results will improve our understanding of the exotic phenomena that can arise in the presence of both disorder and electronic correlations, and will help interpret results of future experiments with disordered optical lattices. The data obtained, especially in the strong-coupling regimes, can also be used to benchmark other numerical methods for disordered fermionic systems. The activities will provide several undergraduate students from the diverse population of San Jose State University with hands-on research experience in the field of computational condensed matter physics, and with opportunities to improve their scientific communication skills through writing papers and presenting their findings at national scientific meetings. The award also supports the PI in his efforts to integrate research and undergraduate education through the incorporation of computational methods into physics courses.

非技术摘要这一奖项支持疾病物理学的理论研究和教育及其对电子如何在真实材料中组织的影响。理论研究和对在低温下表现出意外且经常具有技术有用特性的固体基本特性的理解和理解通常取决于原子形成完美周期性晶格的假设。但是，在研究电子特性时，实际材料中存在的疾病（晶体缺陷或杂质）不可忽略。与系统中的所有其他重要参与者（晶格几何形状，电子之间的相互作用等）一起，它们的存在可以将系统驱动到整个相机，如果仅考虑单独考虑混乱或仅电子相互作用，则不会出现。使用当前数值技术对这种包容系统的准确描述可能是一项艰巨的任务。在该项目中，PI将实施一个新颖的想法，以在某些相互作用电子的数值模拟中有效考虑随机疾病。 PI将使用该方法研究电子的集体重排及其可以进行的不同变换。结果将有助于解释实验观察结果，并最终有助于了解创建外来阶段的机制，例如绝缘和超导阶段，并在技术和能源领域中使用了可能的应用。这些活动将为来自圣何塞州立大学多样化人群的几名本科生提供在计算凝结物理学领域的动手研究经验，并有机会通过撰写论文并在国家科学会议上介绍他们的发现来提高其科学沟通技巧。该奖项还支持PI通过将计算方法纳入物理课程来整合研究和本科教育的努力。技术摘要这一奖项支持理论研究和教育障碍物理及其对电子期过渡的影响。由真实材料中的杂质或晶体缺陷引起的疾病相互作用，而凝结物理学中的电子相关性仅被鲜为人知。关于疾病对相变的外观和性质的影响，以及在不同维度引入电子相互作用时的命运以及对安德森本地化的命运方面的重要问题。对于费米子系统和相应的量子晶格模型尤其如此，这些模型通过随机位点或键能模仿障碍效应。在光学晶格上使用超低费米气体进行的最新实验已经开始阐明其中一些问题。但是，就像在具有干净晶格的实验模拟中一样，这些实验依赖于无近似且高度精确的数值模拟来进行温度计和表征。在该项目中，PI将在数值链接群集扩展中实施一个新的想法，以治疗连续的随机疾病，这是一种新兴而有力的方法，可在热力学极限下产生与强烈相关的电子系统的确切有限温度结果。使用这种方法，PI将研究热力学特性，包括两个和三个维度的海森堡和哈伯德模型的各种磁性和/或超导相关性。结果将提高我们对在疾病和电子相关性存在下可能出现的外来现象的理解，并将有助于解释未来的光学晶格实验的结果。获得的数据，尤其是在强耦合方案中，也可以用于基准用于烦恼的费米子系统的其他数值方法。这些活动将为来自圣何塞州立大学多样化人群的几名本科生提供在计算凝结物理学领域的动手研究经验，并有机会通过撰写论文并在国家科学会议上介绍他们的发现来提高其科学沟通技巧。该奖项还支持PI通过将计算方法纳入物理课程来整合研究和本科教育的努力。