Topological phases of matter and disordered systems

非技术总结该奖项支持理论研究和教育，以研究和了解物质的性质和可能的相，特别是材料和工程材料结构中的电子组成的物质，在不同的条件下。物质的拓扑相在理论上预计会出现在各种材料和材料系统中。重要的例子包括在高磁场中捕获在工程半导体界面上的二维电子液体，被称为拓扑绝缘体的特定绝缘体，以及某些类型的超导体。超导体是一些材料中的一种电子状态，具有独特的量子力学性质，可以无损耗地传输电力。拓扑相的特性是健壮的，因此它们不容易被缺陷和缺陷破坏，但它们不像更传统的相那样与对称性联系在一起。理解拓扑相在本质上需要量子力学理论。实验已经发现或证实了某些拓扑相的存在。这些阶段的物质有很大的潜力引领或促进新技术，包括自旋电子器件，它不仅利用电子的电荷，而且利用电子的内在磁性进行操作，以及在未来基于量子力学状态操纵的计算机技术中。PI将在他之前工作的基础上，进一步发展这些阶段的理论，做出可以在实验中检验的理论预测，或者使其有可能在发生时识别拓扑阶段。具体的重点领域包括将拓扑相模拟为网络的方法，以及在这些系统中的一些系统中出现的一种不寻常的粘度形式。在物质的其他相中，无序，或者固体中普遍存在的随机杂质或缺陷的影响，可以再次导致物质的不同相。该项目将促进对这些，特别是“自旋玻璃”的理论理解。在这些系统中的任何一个给定的例子中，都很难猜测最低能量状态是什么，因为有许多低能量的替代方案。量化这些项目的数量是一个研究课题。从根本上说，这些玻璃系统与网络的许多其他应用以及计算机编程中的优化有关。技术总结该奖项支持拓扑相和无序材料的理论研究和教育。将考虑拓扑阶段的基本方面，以及应用程序和诊断工具。PI将在拓扑相的背景下研究纠缠。PI计划继续研究物质手性拓扑相的张量网络状态；例如，张量网络在一维分类拓扑相方面取得了丰硕成果。他的目标是研究与基本拓扑性质有关的输运现象，如“中心电荷”，以及在量子霍尔系统中测量霍尔粘度的可能性。关于无序系统：PI将使用复制对称破缺理论在短程伊辛自旋玻璃模型中产生关于低温自旋玻璃相中纯态数量的结果，以及其他结果。这涉及自旋玻璃理论中有关纯态的数目和组织的基本概念问题，并且是一个有争议的主题。

NONTECHNICAL SUMMARYThis award supports theoretical research and education to study and understand the properties and possible phases of matter, particularly matter made of electrons in materials and in engineered materials structures, under different conditions. Topological phases of matter are theoretically expected to occur in various materials and materials systems. Important examples include a two-dimensional liquid of electrons trapped at engineered semiconductor interfaces in a high magnetic field, specific insulators known as topological insulators, and in some types of superconductors. Superconductors are a state of electrons in some materials that have distinctive quantum mechanical properties and can transport electricity without loss. Topological phases are characterized by properties that are robust, so they cannot be easily destroyed by imperfections and defects, but they are not connected with symmetries as would be the case in more traditional phases. Understanding topological phases requires the theory of quantum mechanics in an essential way. Experiments have discovered or confirmed the existence of some topological phases. There is great potential for these phases of matter to lead or contribute to new technologies, including spintronic devices which exploit not only on the electron's charge but also its intrinsic magnetic properties for their operation, and in future computer technologies based on the manipulation of quantum mechanical states. The PI will build on his previous work and further develop the theory of these phases, making theoretical predictions that can be tested in experiments or make it possible to identify topological phases as they occur. The specific areas of focus include methods for modeling topological phases as networks, and an unusual form of viscosity that arises in some of these systems.In other phases of matter, disorder, or the effects of random impurities or defects that are endemic in solids, can lead again to distinct phases of matter. This project will advance the theoretical understanding of these, especially "spin glasses." In any given example of one of these systems it is very difficult to guess what the lowest energy state is, because there are many low-energy alternatives. Quantifying the number of these is a topic of research. In a fundamental way, these glassy systems are related to many other applications of networks, and to optimization in computer programming. TECHNICAL SUMMARYThis award supports theoretical research and education on topological phases and disordered materials. Fundamental aspects of topological phases will be considered, as well as applications and diagnostic tools. The PI will investigate entanglement in the context of topological phases. The PI plans to continue work on tensor network states for chiral topological phases of matter; tensor networks have been fruitful in, for example, classifying topological phases in one dimension. He aims to engage the problem of transport phenomena that are related to basic topological properties such as the "central charge," and the possibility of measuring the Hall viscosity in quantum Hall systems. On disordered systems: the PI will use replica symmetry breaking theory to produce results on the number of pure states in the spin-glass phase at low temperatures in the short-range Ising spin glass model, and others. This relates to basic conceptual issues in spin glass theory concerning the number and organization of pure states, and is a subject of controversy.