Novel Ordered States of Electrons

该奖项支持致力于一些丰富和复杂的物质状态的理论研究，其中电子可以在固体中组织自己。 这项工作的智力价值来自其主要目标：这些状态的普遍性质的表征;它们的实验签名的阐明;以及它们可以发生的特定材料和条件的确定。 这项工作将集中在三个主要类别的国家。(1)杂质存在时相互作用电子气的有序态。 我们的目标是更好地理解电子在二维和三维的相图作为无序强度和电子间距的函数。 一个特别吸引人的可能性是，随机杂质实际上可能促进电子有序的发展。(2)非零角动量的密度波态。 目标是阐明它们与超导性和磁性的相互作用，以及它们作为“隐藏”秩序的可能作用，这些秩序导致相关电子材料中令人困惑的行为。 大量的实验和理论兴趣集中在确定铜氧化物超导体中是否出现d密度波序上。 (3)量子磁体、量子点阵列和约瑟夫森结阵列的非阿贝尔拓扑态。 如果在自然界中实现具有非阿贝尔编织统计的系统，这将是量子计算的一个有吸引力的竞技场，因为这种类型的编织统计的丰富性允许通过编织操作进行通用计算，并且因为量子信息被编码在拓扑关系中，这些拓扑关系自动保护免受退相干的局部影响。 然而，人们对这种状态发生的条件知之甚少。 这个项目的主要目的是阐明这个问题。 研究将与教学和培训相结合。 PI还计划完成一本从现代角度看量子凝聚态理论的教科书。%该奖项支持致力于一些丰富和复杂的物质状态的理论研究，其中电子可以在固体中组织自己。 这项工作的智力价值来自其主要目标：这些状态的普遍性质的表征;它们的实验签名的阐明;以及它们可以发生的特定材料和条件的确定。 研究将与教学和培训相结合。 PI还计划从现代角度完成一本关于量子凝聚态理论的教科书。

This award supports theoretical research that is devoted to some of the rich and complex states of matter in which electrons can organize themselves in solids. The intellectual merits of the work drive from its main goals: a characterization of the universal properties of these states; an elucidation of their experimental signatures; and a determination of the particular materials in which, and the conditions under which, they can occur. This work will focus on three primary classes of states. (1) Ordered states of the interacting electron gas in the presence of impurities. The goal is a better understanding of the phase diagrams of electrons in two- and three-dimensions as a function of disorder strength and inter-electron spacing. One particularly fascinating possibility is that random impurities may actually facilitate the development of electronic ordering. (2) Density-wave states of non-zero angular momentum. The goal is to elucidate their interplay with superconductivity and magnetism, and their possible role as 'hidden' orders which lead to puzzling behavior in correlated electron materials. Considerable experimental and theoretical interest is focused on determining whether d-density wave order occurs in the cuprate superconductors. (3) Non-Abelian topological states of quantum magnets, quantum dot arrays, and Josephson junction arrays. If a system with non-Abelian braiding statistics were realized in nature, it would be an attractive arena for quantum computation because the richness of this type of braiding statistics permits universal computation through braiding operations and because the quantum information is encoded in topological relations which are automatically protected against the local effects of decoherence. However, very little is known about the conditions under which such states occur. The principle aim of this project is to shed light on this question. The research will be integrated with teaching and training. The PI also plans to complete a textbook on quantum condensed matter theory from a modern perspective.%%%This award supports theoretical research that is devoted to some of the rich and complex states of matter in which electrons can organize themselves in solids. The intellectual merits of the work drive from its main goals: a characterization of the universal properties of these states; an elucidation of their experimental signatures; and a determination of the particular materials in which, and the conditions under which, they can occur. The research will be integrated with teaching and training. The PI also plans to complete a textbook on quantum condensed matter theory from a modern perspective.***