Physical Properties of Strongly Correlated Quantum Liquids

技术综述：该奖项支持凝聚态物理的理论研究和教育，重点是更深入地理解物质状态下的秩序概念。在序参数概念、Ginzburg-Landau理论和群论的基础上，发展了对称破缺有序的综合理论。这一理论构成了凝聚态理论的基石。PI提出了超越标准Landau-Ginzburg相变理论的拓扑序和量子序的概念。在这个研究项目中，PI计划发展一种更完整的拓扑/量子有序理论。具体地说，PI计划将弦-网平均场理论应用于现实的量子自旋系统，以识别可能包含非平凡拓扑/量子有序的材料。我们将研究弦末端的强烈涨落及其与拓扑态之间的连续跃迁的密切联系。这可能导致拓扑相变的一般理论，其中与弦末端相关的射影对称性可能起到关键作用。特别是，拓扑相变可能导致双层系统中的非阿贝尔FQH态，从而实现普适的量子计算。弦凝聚态的涌现规范理论也可能是理解高温超导体新性质的关键。PI计划使用新发展的自旋-掺杂子理论来更定量地了解高温超导体。这项研究的一个主题是在拓扑/量子有序的一般理论和实验观测之间建立更紧密的联系，例如高温超导体中的那些似乎违反传统解释的实验观测。这项研究还可能导致对新材料和新现象的预测。非技术总结：该奖项支持基础理论凝聚态物理的研究和教育。秩序的概念是我们理解周围世界的重要基石。当含有原子的液体凝固时，原子可能会以周期性的排列方式组织起来，形成晶格。这是物质有序状态的一个例子；在我们周围的世界中，还有许多其他不同的例子，一些更奇特和微妙的例子，可以用标准的相变理论来组织和描述。新材料的发现，如高温超导体，以及当电子在强磁场中被限制在二维空间时出现的量子霍尔相等物质状态的发现，引发了关于秩序的基本性质的问题，以及这个概念是否比我们目前的概念更普遍。PI提出了一种特定的新秩序，这种秩序没有包含在相变的标准理论中，但它将对我们如何理解各种奇异材料中令人费解的实验产生重大影响。该奖项支持旨在发展涉及这些新有序状态的转换理论并发现这一想法的有效性和后果的研究。这项工作可能导致对新现象和可能的新物质状态的预测；对未来技术和其他学科的潜在影响无法估计。这个项目还涉及到学生，并将有助于培养下一代凝聚态理论家。

TECHNICAL SUMMARY:This award supports theoretical research and education in condensed matter physics with an emphasis on a deeper understanding of the notion of order in states of matter. A comprehensive theory for symmetry breaking order has been developed, based on the concept of an order parameter, Ginzburg-Landau theory, and group theory. Such a theory forms a corner stone in the foundation of condensed matter theory. The PI has proposed the concepts of topological order and quantum order that are outside the standard Landau-Ginzburg theory of phase transitions. In this research project, the PI plans to develop a more complete theory of topological/quantum order. Specifically, the PI plans to apply the string-net mean-field theory to realistic quantum spin systems to identify materials that may contain non-trivial topological/quantum order. Strong fluctuations of ends of string and their close tie to the continuous transition between topological states will be studied. This may lead to a general theory for topological phase transitions, where the projective symmetry associated with the ends of string may play a key role. In particular, Topological phase transitions may lead to non-Abelian FQH states in double-layer systems which can realize universal quantum computations. The emergent gauge theory in string condensed states may also be the key to understand the novel properties of high temperature superconductors. The PI plans to use a newly developed spinon-dopon theory to gain a more quantitative understanding of high temperature superconductors.A theme of the research is to build a closer connection between the general theory of topological/quantum order and experimental observations, such as those in high temperature superconductors, that appear to defy a conventional explanation. This research may also lead to predictions of new materials and new phenomena. NON-TECHNICAL SUMMARY:This award supports research and education in fundamental theoretical condensed matter physics. The notion of order is an important cornerstone in the foundation of our understanding of the world around us. When liquid with atoms solidifies, the atoms may organize themselves in a periodic array to form a crystal lattice. This is an example of an ordered state of matter; there are many other diverse examples, some more exotic and subtle, in the world around us that can be organized and described by standard theory of phase transitions. The discovery of new materials, like the high temperature superconductors, and states of matter like the quantum Hall phases that arise when electrons are confined to two dimensions in a high magnetic field, has led to questions about fundamental nature of order and whether the concept is more general than our current notion. The PI proposes a specific new kind of order that is not contained in the standard theory of phase transitions, but yet would have significant consequences on how we understand puzzling experiments in various exotic materials. This award supports research that aims to develop a theory of transformations involving these new ordered states and to discover the validity and consequences of this idea. Predictions of new phenomena and possible new states of matter may result from this work; the potential impact on future technologies and other disciplines cannot be estimated. This project also involves students and will help train the next generation of condensed matter theorists.