Physical Properties of Strongly Correlated Quantum Liquids

强相关量子液体的物理性质

• 批准号: 1005541
• 负责人: Xiao-Gang Wen
• 金额: $ 46.5万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1005541&HistoricalAwards=false
• 关键词: Physical; Properties; Strongly; Correlated; Quantum

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.

技术摘要这一奖项支持有关秩序概念的理论研究和教育，这是凝结物理学的基本概念。过去20年的研究表明，兰道的对称性破坏理论仅描述了可能实现的可能有序状态的一部分。物质的可能有序状态可能比以前想象的要丰富得多。 PI介绍了拓扑顺序和量子顺序的概念，以描述不包含破碎的对称性概念所包含的新的有序状态类型。在这个项目中，PI计划继续他对拓扑/量子顺序的研究，并致力于为这些顺序建立综合理论。特别是，PI将在以下领域中工作：（a）基于字符串 - 网格图片，PI基于张量类别理论开发了针对非手续拓扑秩序的综合理论。 PI计划结合二级模式方法，顶点代数方法以及从射影构建中的有效理论方法，以开发量子霍尔国家的手性拓扑秩序的全面理论。这将使非亚伯量子霍尔国家的阶段和相变的研究能够研究，并能够预测新的非亚伯利亚状态，例如在双层系统中。（b）PI计划开发基于张量网络的新方法。先前的工作证明了张量网络方法在获得拓扑阶段和拓扑相变的有效性。先前的工作还揭示了人们需要改善张量网络方法的指示。 PI计划使用新的方法研究沮丧的量子系统，以发现实际材料中的更多拓扑阶段。（c）PI计划研究一类新的拓扑阶段，对称性受保护的拓扑阶段，这仅适用于具有某些对称性的汉密尔顿人。这些阶段的初步理论是基于投影对称群的。 Spin-1链和拓扑绝缘子/超导体的Haldane相是对称受保护拓扑阶段的特殊例子。 PI计划专注于界面上的相变和无间隙状态。这样的研究可能会导致拓扑阶段的设备应用。PI的拓扑/量子顺序的新兴理论具有对许多物理和数学领域的高影响。拟议的研究将为计算强相关系统的相图提供新的方法。预测拓扑/量子阶段在传统方法的范围之内。该项目将培训学生的高级方法和理论凝结物理物理学的概念。非技术摘要这一奖项支持理论研究和教育，扩展了材料的基本概念。 秩序的概念是我们对周围世界的理解的基础。例如，当液体变为固体时，原子可以在周期性阵列中组织自身以形成晶格。这是有序状态的一个例子；还有许多其他不同的例子，有些异国情调和微妙。它们可以组织起来，并由相变的标准理论描述。新材料和相的发现，例如高温超导体或量子大厅相，当电子局限于高磁场中的两个维度时，就会引起有关顺序的基本性质以及秩序概念是否更一般的问题。 PI提出了标准过渡的标准理论中不包含的新秩序，但对我们如何理解材料会产生重大影响。该奖项支持旨在进一步发展涉及这些新有序国家的转型理论并发现新的物质状态的研究。这项工作也可能导致与新材料相关现象的理论预测。该项目影响我们如何理解周围的世界，并可能对未来的技术和其他科学学科产生潜在的影响。利用其中一些物质形成计算基础的可能性提供了一种可能影响信息技术影响的量子计算机的方法。该项目还涉及学生，并将帮助培训下一代冷凝的物质理论家在高级概念和技术中。