RUI-Anisotropic Phases of Correlated Electronic Systems

该奖项支持理论和计算研究和教育，以促进对低维和极端量子条件下强相关电子系统各向异性相的理解。PI旨在了解具有液晶有序的相关电子系统的各向异性相的起源和稳定机制。相互作用的量子系统在没有不受控制的近似的情况下，无论是在解析上还是在数值上都是难以处理的。PI的重点将放在相关电子系统的微观模型上，这些系统最初表现为费米液体或量子霍尔液体行为，但可能经历相变到非均匀各向异性相。量子多体物理的分析理论方法将与微观模型的无偏数值模拟相结合，为理论理解低维相关电子系统中出现的新型液晶或混合相的性质提供基础。研究重点包括：1)确定相互作用势在各向异性费米液相稳定中的作用；2)了解砷化镓半导体中各向异性压电相互作用；3)研究高朗道能级各向异性相的性质，研究具有破旋对称性的新型液晶态；4)强相互作用驱动的新型电子量子相。该奖项支持本科生的教育机会。本科生将能够参与有价值的研究经验。该奖项将有助于为本科生开发研究机会，并将为少数族裔HBCU机构中代表性不足的学生加强研究和教育基础设施。PI设计的外联活动旨在培养当地社区和当地高中K-12年级学生对科学相关领域的兴趣。该奖项支持理论研究和教育，旨在理解和探索物质的新状态，这些状态是由限于二维材料中相互强烈相互作用的电子产生的。许多相互作用的粒子的量子物理学构成了我们对世界各地实验室合成的复杂材料性质的理解的基础。预测新材料特性和新材料相关现象的能力在寻找未来技术的基石方面发挥着至关重要的作用。电子之间的相互作用导致了有趣的量子力学状态。这些状态中的一些被认为是在长分子系统中观察到的相的量子力学类似物，在这些系统中，分子的方向变得相互关联，就像在液晶显示器中发生的那样。对这些液晶电子状态的理解以及它们在特定情况下的表现不仅从基础科学的角度来看是非常有趣的，而且因为它们可以作为电子设备，传感器，计算等未来技术的潜在构建块。预测新材料特性和新材料相关现象的能力在寻找未来技术的基石方面发挥着至关重要的作用。利用量子多体系统的理论方法，PI将解决在温度接近绝对零度的各种电子系统中发展的各向异性的本质。这个项目的重点是应用计算方法，使计算机能够提供量子力学系统的基本见解。本科生将能够参与有价值的研究经验，并将参与这项研究的重要方面。由于研究需要探索多种模型和方法，因此本科生有很多机会获得重要的研究经验。该奖项将有助于为少数族裔学生加强研究和教育基础设施。通过外展活动，PI旨在培养当地社区和高中K-12年级学生对科学相关领域的兴趣。

TECHNICAL SUMMARYThis award supports theoretical and computational research and education to advance understanding of anisotropic phases of strongly correlated electron systems in low dimensions and under extreme quantum conditions.The PI aims to understand the origin of and the stabilization mechanism for anisotropic phases of correlated electronic systems that possess liquid crystalline order. Interacting quantum systems are often intractable either analytically or numerically without making uncontrolled approximations. The PI's focus will be on microscopic models of correlated electronic systems that originally manifest Fermi liquid or quantum Hall liquid behavior but may undergo phase transitions to inhomogeneous anisotropic phases. Analytical theoretical methods of quantum many-body physics will be used in combination with unbiased numerical simulations of microscopic models to provide a basis for a theoretical understanding of the nature of novel liquid crystalline or hybrid phases that arise in correlated electronic systems in low dimensions. Key foci of the research include:1) Determining the role of interaction potentials in the stabilization of anisotropic Fermi liquid phases,2) Understanding the anisotropic piezoelectric interaction in gallium arsenide semiconductors,3) Investigating the nature of anisotropic phases in high Landau levels in terms of novel liquid crystalline states with broken rotational symmetry,4) Novel electronic quantum phases driven by strong interactions.This award supports educational opportunities for undergraduate students. Undergraduate students will be able to participate in valuable research experiences. This award will help to develop research opportunities for undergraduate students and will enhance research and education infrastructure for underrepresented students at a minority HBCU institution. The outreach activities devised by the PI are aimed to develop interest in science related areas at the K-12 level in local communities and local high schools.NONTECHNICAL SUMMARYThis award supports theoretical research and education aimed at understanding and exploring new states of matter that arise from electrons that interact strongly with each other in materials confined to two dimensions. Quantum physics of many interacting particles forms the basis of our understanding of the properties of complex materials synthesized in laboratories all over the world. The ability to predict the properties of new materials and new materials-related phenomena can play a crucial role in the search for the building blocks of future technologies. The interaction between electrons leads to intriguing quantum mechanical states. Some of these states are believed to be quantum mechanical analogs of phases observed in systems of long molecules in which the orientation of the molecules become correlated with each other, as occurs in, for example, a liquid crystal display. The understanding of these liquid-crystal-like states of electrons and how they appear under specific circumstances is of great interest not only from the perspective of fundamental science, but also because they serve as potential building blocks of future technologies for electronic devices, sensors, computation, and more. The ability to predict the properties of new materials and new materials-related phenomena can play a crucial role in the search for the building blocks of future technologies. Using theoretical methods for quantum many-body systems, the PI will address both the nature of the anisotropy that develops in a variety of electronic systems at temperatures close to the absolute zero of temperature. This project includes a focus on applying computational methods to enable computers to provide fundamental insight into quantum mechanical systems. Undergraduate students will be able to participate in valuable research experiences and will be involved in important aspects of this research. Because the research requires exploring a variety of models and methods, there are many opportunities for undergraduate students to gain important research experience. This award will help to enhance research and education infrastructure for underrepresented minority students. Through an outreach activity, the PI aims to develop interest in science related areas at the K-12 level in local communities and high schools.