RUI: Disorder in Strongly-Correlated Electrons on a Lattice

非技术性总结该奖项支持无序物理学及其对电子如何在真实的材料中组织的影响的理论研究和教育。理论研究和理解的基本性质的固体表现出意想不到的，往往是技术上有用的性质在低温下通常依赖于假设原子形成完美的周期性晶格。然而，在研究电子性质时，存在于真实的材料中的无序（晶体缺陷或杂质）总是不能忽略的。连同系统中的所有其他重要角色（晶格几何形状、电子之间的相互作用等），它们的存在可以将系统作为一个整体驱动到如果只考虑无序或只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将实现一个新的想法，在相互作用的电子的某些数值模拟中有效地考虑随机无序。PI将使用该方法来研究电子的集体重排以及它们可以经历的不同转变。这些结果将有助于解释实验观察结果，并最终有助于理解创造奇异相（如绝缘相和超导相）背后的机制，并可能在技术和能源领域应用。这些活动将为来自圣何塞州立大学不同人群的几名本科生提供计算凝聚态物理学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研究结果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来整合研究和本科教育的努力。该奖项支持无序物理学及其对电子相变的影响的理论研究和教育。人们对真实的材料中的杂质或晶体缺陷引起的无序与凝聚态物理学中的电子相关性的相互作用知之甚少。关于无序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后安德森局域化的命运等重要问题，在很大程度上仍然没有解决。这对于费米子系统和相应的量子晶格模型来说尤其如此，这些模型通过随机位置或键能来模拟无序效应。最近在光学晶格上进行的超冷费米气体实验已经开始揭示其中的一些问题。然而，与使用干净晶格的实验模拟非常相似，这些实验依赖于近似自由和高度精确的数值模拟来进行测温和表征。在这个项目中，PI将实施一个新的想法，用于处理连续随机无序的数值连接簇膨胀，一个新兴的和强大的方法，产生精确的有限温度的结果，强相关的电子系统在热力学极限。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。这些结果将提高我们对无序和电子关联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，特别是在强耦合制度，也可以用来衡量其他数值方法的无序费米子系统。这些活动将为来自圣何塞州立大学不同人群的几名本科生提供计算凝聚态物理学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研究结果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来整合研究和本科教育的努力。

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.