Quantum Phases in Condensed Matter

Dmr-9800626 Shankar这是一笔资助理论凝聚态物理研究以及教育活动的拨款。 研究将集中在两个领域的巨大电流感兴趣：场论的分数量子霍尔效应和重整化群相变。 一本关于场论在凝聚态物质中的应用的教科书也正在编写中。 自从二维电子气的霍尔电导被量子化为某些分数值这一引人注目的发现以来，一直有一系列旨在解释这一现象的许多方面的理论工作。 虽然有一个令人印象深刻的知识体系，但仍然缺乏一个单一的微观理论来描述所有这些部分，从磁场中的电子开始，受到库仑相互作用和随机衬底势的影响。 陈-西蒙斯场论是最有希望的选择之一，在这种场论中，人们把电子映射到玻色子或费米子中，平均来说，玻色子或费米子要么看不到场，要么看到一个较弱的场，它们填充了整数个朗道能级。 基于这些理论的框架已经开发。 它以一种连贯的方式再现了许多已知的结果，一些特殊的分数（其中净场为零）从上述的出发点，并承诺产生更多的结果，为其他分数。 由于在许多方面与其他方法有很大的不同，这种分析要么不同意某些现有的结果，要么提供一个完全独立的确认，特别是对于半满的情况。 前一段时间提出了费米子的重整化群方案，其中系统地消除费米面附近的模以提取低能物理。 在这个方案中，朗道的费米液体表现为一个固定点，而不稳定性，即超导性则表现为相关的流动。 不幸的是，这种方法仅限于零耦合时的跃迁. 有限耦合的扩展通常涉及费米子以及由它们形成的玻色子场。 一个计划，其中高能量模式的两个并排消除，迄今已被证明是难以捉摸的，将进行调查。 该补助金将支持凝聚态理论的研究以及研究生教科书的写作。 该研究的重点是场论技术的应用，目前感兴趣的凝聚态物理问题。 这些问题包括分数量子霍尔效应的研究-一种新的物质状态。 这项工作的成功完成将对凝聚态物理和材料物理产生广泛的影响。 ***

Dmr-9800626 Shankar This is a grant to fund research in theoretical condensed matter physics, as well as educational activities. The research will focus on two areas of great current interest: field theory of the fractional quantum Hall effect and renormalization group for phase transitions. A textbook is also being written on the application of field theory to condensed matter. Since the remarkable discovery that the Hall conductance of a two-dimensional electron gas is quantized to some fractional values, there has been a steady stream of theoretical work aimed at explaining many aspects of this phenomenon. While there is an impressive body of knowledge, one still lacks a single microscopic theory that will describe all these fractions, starting from just electrons in a magnetic field, subject to Coulomb interactions and the random substrate potential. Chern-Simons field theories, in which one maps electrons into either bosons or fermions which, on the average, see either no field or a weaker field in which they fill an integer number of Landau levels, are one of the most promising options. A framework based on these theories has been developed. It reproduces in a coherent way many known results for some special fractions (in which the net field vanishes) from the above mentioned starting point and promises to yield more results for the other fractions. Being very different in many ways from other techniques used, this analysis will either disagree with some existing results or provide a totally independent confirmation, especially for the half-filled case. Some time ago a renormalization group scheme for fermions was worked out in which one systematically eliminates modes near the Fermi surface to extract the low energy physics. In this scheme Landau's Fermi liquid appears as a fixed point, while instabilities, to say, superconductivity emerge as relevant flows. Unfortunately, the method has been limited to transitions that occur at zero couplin g. Extension to finite coupling typically involves the fermions one begins with as well as bosonic fields formed out of them. A scheme in which high energy modes of both are eliminated side by side, and which has so far proven elusive, will be investigated. %%% This grant will support research on condensed matter theory as well as the writing of a graduate textbook. The research focuses on the application of field theoretical techniques to problems of current interest in condensed matter physics. These problems include the study of the fractional quantum Hall effect - a new state of matter. Successful completion of the proposed work should have wide ranging impact on condensed matter and materials physics. ***