Role of Disorder in Strongly Correlated Low-Dimensional Systems

该奖项支持旨在阐明低维电子系统中电子-电子相互作用和无序之间相互作用的研究和教育。这仍然是现代凝聚态物理中的一个主要而困难的问题。该奖项支持以下研究：分数量子霍尔液体的边缘状态，特别是在存在边缘重建的情况下；无序存在下的体积分数量子霍尔液体，重点研究无序和相互作用对其输运性质和不同量子霍尔相之间的量子相变附近临界行为的影响；二维非s波超导体中以铜酸盐为原型的准粒子输运性质以及量子点和纳米尺寸金属颗粒的磁性和超导特性。PI将在这些调查中结合数值和分析方法。具体方法包括映射到有效场论，精确对角化，和量子蒙特卡罗模拟。数值研究将阐明PI在块状分数量子霍尔液体和超导体准粒子输运性质研究中的多电子波函数和准粒子波函数的拓扑性质，如陈氏数。计算将集中在可以通过实验直接测量的物理量上，并尽可能将我们的结果与实验进行比较。该奖项的广泛影响主要是教育；这项工作包括训练下一代凝聚态理论家。该奖项支持基础研究和教育，旨在促进我们对局限于一维或二维并被缺陷破坏的强相互作用电子的理解。PI将研究各种材料和系统中强相关性和无序的综合效应，包括量子霍尔系统、纳米级铁磁体和超导晶粒。这项基础研究有助于提高对材料中发生的基本和新型电子状态和现象的理解，并有助于潜在的未来电子设备技术的智力基础。该奖项还支持培训下一代凝聚态理论家。

This award supports research and education that aims to elucidate the interplay between electron-electron interaction and disorder in low dimensional electronic systems. This remains a major and difficult problem in modern condensed matter physics. This award supports studies of: edge states of fractional quantum Hall liquids, especially in the presence of edge reconstruction; bulk fractional quantum Hall liquids in the presence of disorder, focusing on the effects of disorder and interaction on their transport properties and critical behavior near the quantum phase transitions between different quantum Hall phases; quasiparticle transport properties in two-dimensional non-s-wave superconductors in the absence of time-reversal symmetry, with the cuprates as the prototype; and magnetic and superconducting properties of quantum dots and nano-size metallic grains. The PI will combine numerical and analytical methods in these investigations. Specific methods include mapping to an effective field theory, exact diagonalization, and quantum Monte Carlo simulation. Numerical studies will elucidate the topological properties, such as Chern numbers, of many-electron wave functions and quasiparticle wave functions in the PI's investigations of bulk fractional quantum Hall liquids and quasiparticle transport properties in superconductors. Calculations will focus on physical quantities that can be directly measured experimentally, and compare our results with experiments whenever possible. The broader impacts of this award are primarily educational; the work involves training the next generation of condensed matter theorists.This award supports fundamental research and education that seeks to advance our understanding of strongly interacting electrons confined to one or two dimensions and disrupted by imperfections. The PI will study the combined effect of strong correlations and disorder in a variety of materials and systems including quantum Hall systems and nanoscale ferromagnets and superconducting grains. This basic research helps improve understanding of fundamental and novel electronic states and phenomena that occur in materials and contributes to the intellectual underpinnings of potential future electronic device technologies. This award also supports training the next generation of condensed matter theorists.