Quantum Hall Effect and Disordered Systems

9818259阅读一般无序系统中物质的低温相和这些相之间的跃迁，特别是具有高垂直磁场的二维电子气中的量子霍尔区，将使用理论方法进行研究。 感兴趣的具体阶段包括量子霍尔效应中的可压缩和不可压缩液体。 这项工作将治疗他们的基本激发，无论是在散装和在边缘，无序效应，不同阶段之间的过渡和普遍的临界特性。 要考虑的其他阶段包括具有淬灭无序的量子自旋系统。 所使用的理论方法将主要是分析，经常基于多体理论和微扰和非微扰量子场论技术。 虽然重点是在基本属性，应用实验将尽可能。 从理论上描述相变和转变将有助于确定哪些相变和转变发生在实验系统中。 这是对先前总统青年研究员奖的延续。%这一先前的总统青年研究员奖的资助更新继续支持多体理论物理学的前沿理论家。 本计画将著重于研究高垂直磁场中二维电子气中电子态的低温行为-量子霍尔区。 另外的工作将在理解量子自旋系统的行为上进行。 这项工作将提高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议题，并在总体上提高我们对多体效应的理论理解，这些多体效应在确定一系列具有技术重要性的电子和磁性材料的特性方面至关重要。

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.***