Physical Properties of Strongly Correlated Quantum Liquids

该奖项支持理论研究和教育的概念，秩序，在凝聚态物理的基本概念。近20年来的研究表明，朗道对称破缺理论只描述了物质可能实现的有序态的一个子集。物质可能的有序状态可能比以前想象的要丰富得多。PI引入了拓扑序和量子序的概念来描述不包含在破缺对称性概念中的新型有序态。在这个项目中，PI计划继续他对拓扑/量子秩序的研究，并致力于为这些秩序建立一个全面的理论。特别地，PI将在以下领域工作：(a)基于弦网图，PI发展了一个基于张量范畴论的非手性拓扑序的综合理论。PI计划将零模式方法、顶点代数方法和射影构造的有效理论方法结合起来，发展量子霍尔态手性拓扑秩序的综合理论。这将使非阿贝尔量子霍尔态的相和相变的研究成为可能，并将使新的非阿贝尔态的预测成为可能，例如在双层系统中。(b) PI计划开发一种基于张量网络的新型方法。先前的工作已经证明了张量网络方法在获得拓扑相位和拓扑相变方面的有效性。之前的工作也揭示了需要改进张量网络方法的方向。PI计划使用新方法来研究受挫的量子系统，以发现真实材料中更多的拓扑相。(c) PI计划研究一类新的拓扑相，对称保护拓扑相，它只存在于具有某些对称性的哈密顿量中。在射影对称群的基础上，提出了这些相的初步理论。自旋-1链和拓扑绝缘体/超导体的霍尔丹相是对称保护拓扑相的特殊例子。PI计划专注于界面上的相变和无间隙状态。这些研究可能会导致拓扑相的器件应用。PI的新兴拓扑/量子秩序理论对物理和数学的许多领域都有很大的影响。所提出的研究将导致计算强相关系统相图的新方法。预测拓扑/量子相位超出了传统方法的范围。本项目将培养学生掌握理论凝聚态物理的先进方法和概念。该奖项支持扩展材料基本概念的理论研究和教育。秩序的概念是我们理解周围世界的重要基石。例如，当液体变成固体时，原子可能以周期性阵列组织自己形成晶格。这是物质有序状态的一个例子；还有许多其他不同的例子，有些更奇特，更微妙。它们可以被组织起来，它们之间的转变可以用标准相变理论来描述。新材料和相的发现，如高温超导体或量子霍尔相，当电子被限制在高磁场的二维空间时，就会出现，这导致了对秩序的基本性质以及秩序的概念是否更普遍的问题。PI提出了相变标准理论中没有包含的新秩序，但对我们如何理解材料具有重要影响。该奖项支持旨在进一步发展涉及这些新有序状态的转换理论和发现物质新有序状态的研究。新材料相关现象的理论预测也可能由此产生。这个项目影响着我们如何理解我们周围的世界，并可能对未来的技术和其他科学学科产生潜在影响。利用这些物质状态中的一些来形成计算基础的可能性，为制造量子计算机提供了一种可能的方法，这将对信息技术产生影响。这个项目也有学生参与，将有助于培养下一代凝聚态理论家的先进概念和技术。

TECHNICAL SUMMARYThis award supports theoretical research and education on the notion of order, a fundamental concept in condensed matter physics. Research in last 20 years suggests that Landau's symmetry breaking theory only describes a subset of possible ordered states that matter can realize. The possible ordered states of matter may be much richer than imagined before. The PI introduced the concepts of topological order and quantum order to describe the new types of ordered states that are not encompassed by the concept of broken symmetry. In this project, the PI plans to continue his research on topological/quantum order and to work towards building a comprehensive theory for these kinds of order. In particular, the PI will work in the following areas:(a) Based on the string-net picture, the PI has developed a comprehensive theory for non-chiral topological order based on the tensor category theory. The PI plans to combine the pattern-of-zeros approach, the vertex algebra approach, and the effective theory approach from projective construction to develop a comprehensive theory for chiral topological order in quantum Hall states. This will enable the study of phases and phase transitions for non-Abelian quantum Hall states and will enable the prediction of new non-Abelian states, for example in double-layer systems.(b) The PI plans to develop a new type of approach based on tensor network. The previous work has demonstrated the effectiveness of tensor network approach in obtaining topological phases and topological phase transitions. The previous work also reveals the directions that one needs to improve the tensor network approach. The PI plans to use the new approach to study frustrated quantum systems to discover more topological phases in real materials.(c) The PI plans to study a new class of topological phases, symmetry protected topological phases, which exist only for Hamiltonians with certain symmetries. A preliminary theory for these phases has been developed based on projective symmetry group. The Haldane phase for spin-1 chain and topological insulators/superconductors are special examples of symmetry protected topological phases. The PI plans to concentrate on phase transitions and gapless states on the interfaces. Such studies may lead to device applications for topological phases.The PI's emerging theory of topological/quantum order has the potential for high impact on many areas of physics and mathematics. The proposed research will result in new approaches for calculating phase diagrams of strongly correlated systems. Predicting topological/quantum phases lies outside the reach of traditional methods. This project will train students in advanced methods and concepts of theoretical condensed matter physics. NONTECHNICAL SUMMARYThis award supports theoretical research and education that extends a fundamental concept of materials. The notion of order is an important cornerstone in the foundation of our understanding of the world around us. For example when a liquid becomes a solid, 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. They can be organized and the transitions among them described by the standard theory of phase transitions. The discoveries of new materials and phases, such as the high temperature superconductors or the quantum Hall phases, which arise when electrons are confined to two dimensions in a high magnetic field, have led to questions about the fundamental nature of order and whether the concept of order is more general. The PI has proposed new kinds of order that are not contained in the standard theory of phase transitions, but yet would have significant consequences on how we understand materials. This award supports research that aims to develop further a theory of transformations involving these new ordered states and to discover new ordered states of matter. The theoretical prediction of new materials-related phenomena may also result from this work. This project influences how we understand the world around us and could have potential impact on future technologies and other scientific disciplines. The possibility of utilizing some of these states of matter to form the basis of computation provides a possible way to make a quantum computer which would have impact on information technology. This project also involves students and will help train the next generation of condensed matter theorists in advanced concepts and techniques.