Emergent Behavior of Microscopic Model Systems

该奖项支持理论研究和教育，以解决长期存在的基本问题，涉及相关电子流体的紧急性质，使用理论物理的良好控制方法。PI将通过仔细分析在晶格尺度上定义的相互作用电子的简化模型的行为来研究电子系统的特性。PI将探索相互作用电子系统的一般特性，并试图通过包含有趣材料的电子结构的显着特征来深入了解强相关电子系统的材料特定特征。PI将采取三管齐下的方法：1。PI将研究在弱耦合极限下相互作用电子的简化模型的行为，在弱耦合极限下，可控的微扰重整化群计算是可能的，并且可以获得渐近精确的结果。为了扩大这些方法所能触及的物理范围，我们将研究微调电子结构。这相当于研究了量子多临界点附近的相和相变的性质。在量子临界点附近，电子性质通常可以用量子场论来描述。量子场论在相关电子系统中的一个特别成功的应用是使用陈-西蒙斯-朗道-金兹伯格理论来描述量子霍尔系统。这种方法暗示了量子霍尔系统的性质与超导体的性质之间的深刻类比。PI将研究陈-西蒙斯-朗道-金兹伯格理论的合理性和适用性限制，并进一步探索超导体和量子霍尔系统之间隐含类比的后果。某些相关材料的特性的特定方面可以通过捕获其局部电子结构的一些基本特征的模型来解决。目标主要是深入了解一种或另一种有趣的实验材料的物理特性。新发现的Cs3C60的反铁磁绝缘态就是一个很好的例子；因为它是绝缘的，所以可以通过展开莫特绝缘状态来研究它，在这种状态下，每个C60分子上的电子数量由有效的哈伯德相互作用固定。了解哪些进一步的相互作用在这个强相关极限中占主导地位，以及它们如何决定有序态的性质，可能会揭示在压力下产生这种材料超导性的相互作用，以及在更广泛的超导材料A3C60家族中，其中A是许多碱金属中的任何一种。了解相关电子流体的特性可能会导致利用新材料特性来开发新设备和新技术的能力，这些新设备和技术的工作原理来自于高度相关电子流体中的新相和相竞争。该奖项支持研究和教育，旨在促进对电子相互作用的材料的理解，这些电子相互作用会产生具有有趣和不寻常性质的电子物质的新状态。这项研究的主要目的是深入了解在强相互作用材料中出现的电子物质状态的本质。PI将使用材料中电子的简化模型来检验从受控理论方法获得的解之间的关系，这些方法假设电子有效地弱相互作用与各种其他方法获得的结果。超导是物质的一种紧急状态，其特点是具有无电阻或无能量损失的导电能力。PI将探索超导体的基本物理和被称为量子霍尔效应的看似非常不同的物质状态之间的有趣联系。当一个二维电子层（可以存在于人工分层的半导体材料中）暴露在垂直磁场中时，量子霍尔效应就会出现。PI的目标是利用超导的知识来获得对量子霍尔效应的基本物理学的新见解。PI还将研究在一种由元素铯和含有60个原子的碳分子组成的材料中出现的超导状态，这种材料在压力下表现出超导性。实验表明，其性质与高温超导体和其他具有强相互作用电子的材料在质量上相似。PI对这种最近发现的超导体的研究可能会导致对高温超导体中超导性质的深入了解。了解相关电子流体的特性可能会导致利用新材料特性来开发新设备和新技术的能力，这些新设备和技术的工作原理来自于高度相关电子流体中的新相和相竞争。

TECHNICAL SUMMARYThis award supports theoretical research and education to address long-standing fundamental problems concerning the emergent properties of correlated electron fluids using well-controlled methods of theoretical physics. The PI will investigate properties of electronic systems through a careful analysis of the behavior of simplified models of interacting electrons defined at the lattice scale. The PI will explore generic properties of interacting electronic systems and also attempt to gain insights into material specific features of strongly correlated electronic systems through the inclusion of salient features of the electronic structure of interesting materials. The PI will pursue a three-pronged approach:1. The PI will study the behavior of simplified models of interacting electrons in the weak-coupling limit where controlled, perturbative renormalization group calculations are possible and asymptotically exact results can be obtained. In order to broaden the scope of the physics accessible by these methods, fine-tuned electronic structures will be investigated. This amounts to studying the properties of the phases and phase transitions in the vicinity of quantum multicritical point.2. Near a quantum critical point, electronic properties can often be described by a quantum field theory. A particularly successful use of quantum field theory in correlated electron systems has been the use of Chern-Simons Landau Ginzberg theory to describe quantum Hall systems. This approach implies a profound analogy between the properties of quantum Hall systems and the properties of superconductors. The PI will study the justification and limits of applicability of the Chern-Simons Landau Ginzberg theory, and further explore the consequences of the implied analogy between superconductors and quantum Hall systems.3. Specific aspects of the properties of certain correlated materials can be addressed in terms of models that capture some essential feature of their local electronic structure. The goal is mainly to gain insights into the physics of one experimentally interesting material or another. A good example is provided by the newly discovered antiferromagnetic insulating state of Cs3C60; because it is insulating, it can be studied by expanding about a Mott insulating state in which the number of electrons on each C60 molecule is fixed by the effective Hubbard interaction. Understanding which further interactions dominate in this strongly correlated limit, and how they determine the nature of the ordered states may shed light on the interactions that give rise to superconductivity of this material under pressure, and in the broader family of superconducting materials A3C60, where A is any of a number of alkali metals.Understanding the properties of correlated electron fluids may lead to the ability to exploit novel materials properties to develop new devices and technologies that derive their operating principles from the novel phases and phase competitions that occur in highly correlated electron fluids.NON TECHNICAL SUMMARYThis award supports research and education with an aim to advance understanding of materials with electrons that interact strongly with each other giving rise to new states of electronic matter with interesting and unusual properties. The broad thrust of this research is to gain insights into the nature of the states of electronic matter that emerge in strongly interacting materials. The PI will use simplified models for electrons in materials to examine the relationship between solutions obtained from controlled theoretical methods that assume that electrons are effectively weakly interacting to results obtained by various other methods. Superconductivity is one kind of emergent state of matter which is characterized by the ability of conduct electricity without resistance or loss of energy. The PI will explore an interesting connection between the fundamental physics of superconductors and the seemingly very different state of matter known as the quantum Hall effect. The quantum Hall effect arises when a two-dimensional layer of electrons, which can exist in an artificially layered semiconductor material, is exposed to a perpendicular magnetic field. The PI aims to exploit knowledge of superconductivity to gain new insights into the fundamental physics of the quantum Hall effect.The PI will also investigate the superconducting state that emerges in a material composed of the element cesium and a molecule of carbon containing 60 atoms which exhibits superconductivity under pressure. Experiments reveal properties that are qualitatively similar to those of the high temperature superconductors and other materials with strongly interacting electrons. The PI's study of this recently discovered superconductor may lead to insights into the nature of superconductivity in the high temperature superconductors.Understanding the properties of correlated electron fluids may lead to the ability to exploit novel materials properties to develop new devices and technologies that derive their operating principles from the novel phases and phase competitions that occur in highly correlated electron fluids.