RUI: Disorder in Strongly-Correlated Electrons on a Lattice

该奖项支持在无序物理学及其对电子在真实材料中如何组织的影响方面的理论研究和教育。固体在低温下表现出意想不到的、通常在技术上有用的特性，对固体基本特性的理论研究和理解通常依赖于原子形成完美周期性晶格的假设。然而，在研究电子性质时，真实材料中存在的无序（晶体缺陷或杂质）总是不能被忽视的。与系统中所有其他重要的参与者（晶格几何，电子之间的相互作用等）一起，它们的存在可以将系统作为一个整体驱动到如果单独考虑无序或仅考虑电子相互作用则不会出现的阶段。使用当前的数值技术准确描述这样一个包容性系统可能是一项艰巨的任务。在这个项目中，PI将实现一个新颖的想法，在某些相互作用电子的数值模拟中有效地考虑随机无序。PI将使用这种方法来研究电子的集体重排以及它们可能经历的不同转变。这些结果将有助于解释实验观察结果，并最终有助于理解奇异相（如绝缘和超导相）产生背后的机制，并可能在技术和能源领域得到应用。这些活动将为圣何塞州立大学的几名本科生提供在计算凝聚态物理领域的实践研究经验，并有机会通过撰写论文和在国家科学会议上展示他们的发现来提高他们的科学交流技能。该奖项还支持PI通过将计算方法纳入物理课程，将研究与本科教育相结合的努力。该奖项支持在无序物理学及其对电子相变的影响方面的理论研究和教育。在实际材料中由杂质或晶体缺陷引起的无序与凝聚态物理中的电子相关性之间的相互作用尚不清楚。关于无序对相变的外观和性质的影响的重要问题，以及在不同维度引入电子相互作用时安德森局域化的命运，在很大程度上仍未解决。这对于费米子系统和相应的量子点阵模型来说尤其如此，这些模型通过随机点或键能来模拟无序效应。最近在光学晶格上对超冷费米气体进行的实验已经开始揭示其中的一些问题。然而，就像在干净晶格的实验模拟中一样，这些实验依赖于近似自由和高度精确的温度测量和表征数值模拟。在这个项目中，PI将实现一个处理数值连接簇展开中连续随机无序的新想法，这是一种新兴的强大方法，可以在热力学极限下为强相关电子系统产生精确的有限温度结果。使用这种方法，PI将研究热力学性质，包括海森堡和哈伯德模型在二维和三维中的各种磁性和/或超导相关性。该结果将提高我们对在无序和电子相关存在下可能出现的奇异现象的理解，并将有助于解释未来无序光学晶格实验的结果。所获得的数据，特别是在强耦合情况下的数据，也可用于对无序费米子系统的其他数值方法进行基准测试。这些活动将为圣何塞州立大学的几名本科生提供在计算凝聚态物理领域的实践研究经验，并有机会通过撰写论文和在国家科学会议上展示他们的发现来提高他们的科学交流技能。该奖项还支持PI通过将计算方法纳入物理课程，将研究与本科教育相结合的努力。

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.