Quantum Hall Effect and Disordered Systems

我们将使用理论方法研究无序系统中物质的低温相以及这些相之间的跃迁，特别是在具有高垂直磁场的二维电子气中的量子霍尔区。感兴趣的特定阶段包括量子霍尔效应中的可压缩和不可压缩液体。这项工作将处理它们的基本激发，包括整体和边缘，无序效应，以及不同相之间跃迁的普遍临界性质。其他要考虑的相包括具有猝灭无序的量子自旋系统。所使用的理论方法将主要是解析的，通常基于多体理论以及微扰和非微扰量子场论技术。虽然重点放在基本性质上，但在可能的情况下将应用于实验。从理论上描述这些阶段和转变将有助于确定哪些阶段和转变发生在实验系统中。这是对之前的总统青年研究人员奖的续展。%这项授予延续了以前的总统青年研究人员奖，继续支持多体理论物理学中的一位前沿理论家。本项目将致力于研究二维电子气中电子态在高垂直磁场--量子霍尔区中的低温行为。将在理解量子自旋系统的行为方面开展额外的工作。这项工作将加强我们对分数量子霍尔效应的理解，这是1998年诺贝尔物理学奖的中心主题，并总体上提高我们对多体效应的理论理解，多体效应在决定一系列具有技术重要性的电子和磁性材料的性质方面至关重要。*

9818259ReadThe low-temperature phases of matter and transitions between these phases in disordered systems in general, and in particular the quantum Hall regime in a two-dimensional electron gas with a high perpendicular magnetic field, will be studied using theoretical methods. Specific phases of interest include the compressible and incompressible liquids in the quantum Hall effect. This work will treat their elementary excitations, both in the bulk and at the edge, disorder effects, and universal critical properties of the transitions between distinct phases. Other phases to be considered include quantum spin systems with quenched disorder. The theoretical methods used will be mainly analytical, frequently based on many-body theory and both perturbative and non-perturbative quantum field theoretic techniques. While the emphasis is on fundamental properties, applications to experiment will be made when possible. Characterizing the phases and transitions theoretically will help determine which ones occur in experimental systems. This is a renewal of a prior Presidential Young Investigator award.%%%This grant renewal of a prior Presidential Young Investigator award continues the support of a forefront theorist in many-body theoretical physics. This project will focus on studying low-temperature behavior of electron states in a two-dimensional electron gas in a high perpendicular magnetic field-the quantum Hall regime. Additional work will be carried out on understanding the behavior of quantum spin systems. This work will enhance our understanding of the fractional quantum Hall effect, the central topic of the 1998 Nobel Prize in physics, and in general improve our theoretical understanding of many-body effects that are critical in determining the properties of a range of electronic and magnetic materials of technological importance.***