Topological Phases and Correlation Phenomena in Complex Materials

该奖项支持理论研究和教育，以研究理论凝聚态物理学两个一般领域的几个问题。 第一个研究领域涉及电子和原子系统的拓扑相：PI将研究具有非平凡拓扑的部分填充带的性质和不稳定性，以及如何在表面和界面处创建拓扑状态，例如在3D拓扑绝缘体表面的非常规二维气体中。PI将研究拓扑状态的拓扑或几何场论与合理实验之间的联系。研究的第二个领域是如何结合数值矩阵产品状态方法和分析理论可以导致洞察到一些具有挑战性的问题，在低维强相关物理。 该项目的这一部分的两个目标是了解相互作用无序系统中多体局域化的一维模型，并为一些开放的二维经典或量子统计物理问题开发预测方法。 这一部分建立在以前的工作，了解量子信息理论的概念，如纠缠可以帮助相关材料的数值模拟。这个建议的教育部分是显着的，最大的支出是研究生的支持。 这将有助于发展一支具有科学素养的劳动力队伍。 PI将在大学内开展新课程开发和本科生研究监督，除了他的普通教学负荷和其他地方的高等学校讲座。 对于学术界以外的外联，PI将扩大他的演讲和写作有关凝聚态物理学的最新发展和历史亮点。 非技术总结该奖项支持理论研究和教育，以研究新型电子材料。 近年来，出现了几种新的电子材料。 一个例子是发现了具有原子级薄金属表面的电绝缘体，其对最常见类型的杂质和无序非常鲁棒。 这些新的绝缘体被称为拓扑绝缘体，因为它们的本体绝缘行为和表面金属行为之间的联系是由称为拓扑学的数学分支描述的，拓扑学研究在连续变化下不变的性质。 更常见的绝缘体通常没有表面金属层，即使有，它对无序的稳定性也要差得多。 拓扑绝缘体中坚固的表面金属层的另一个有趣特性是，在层中移动的电子实际上是无质量的，因为它们的能量与它们的动量成线性比例。固体中的电子表现出各种各样的集体现象，包括磁性和超导性。超导性是电子的一种状态，其特征是对电流流动的电阻在低温下消失。 这些集体行为是电子之间相互作用的结果。 该项目的一个目标是了解拓扑绝缘体和相关材料，目前在单个电子的水平上理解，当电子之间的相互作用包括在内时，如何导致新的集体现象。 PI还试图了解如何使用不同材料之间的界面创建新的电子状态。 使用的方法从最初为粒子物理学开发的先进技术到计算模拟，其中从量子信息理论中得出的想法对我们模拟低维系统的能力产生了重大影响。 量子信息概括了经典信息理论，它描述了现代计算机和数据系统的操作，使用特定于量子系统的思想。其中一个重要的概念是纠缠，这是一种微妙的相关性，其中对一个大系统的最佳描述并不意味着对其部分的完整描述。 拓扑序的研究影响了凝聚态物理学的许多其他领域和一些技术领域;它为未来的设备奠定了知识基础。 为了向广大受众传达理论材料研究的重要性和兴奋性，将支持几项教育和推广工作。本提案的教育部分很重要，最大的支出是研究生支持。 这将有助于发展一支具有科学素养的劳动力队伍。 PI将在大学内开展新课程开发和本科生研究监督，除了他的普通教学负荷和其他地方的高等学校讲座。 对于学术界以外的外联，PI将扩大他的演讲和写作有关凝聚态物理学的最新发展和历史亮点

TECHNICAL SUMMARYThis award supports theoretical research and education to study several problems in two general areas of theoretical condensed matter physics. The first area of research concerns topological phases of electronic and atomic systems: the PI will study the properties and instabilities of partially filled bands with nontrivial topology and how topological states could be created at surfaces and interfaces, for example in the unconventional two-dimensional gas at the surface of a 3D topological insulator. The PI will investigate connections between topological or geometric field theories of topological states and plausible experiments. The second area of research is on how a combination of numerical matrix-product-state methods and analytic theory can lead to insights into some challenging problems in strong-correlation physics in low dimensions. The two goals for this section of the project are to understand one-dimensional models of many-body localization in interacting disordered systems, and to develop predictive methods for some open two-dimensional classical or quantum statistical physics problems. This section builds upon previous work on understanding how quantum information theory concepts such as entanglement can aid the numerical simulation of correlated materials.The educational component of this proposal is significant, and the largest expenditure is for graduate student support. This will contribute to the development of a scientifically sophisticated workforce. The PI will carry out new course development and undergraduate student research supervision within the university, in addition to his ordinary teaching load and lectures at advanced schools elsewhere. For outreach beyond the academic community, the PI will expand his lecturing and writing about recent developments and historical highlights of condensed matter physics. NON-TECHNICAL SUMMARYThis award supports theoretical research and education to study new kinds of electronic materials. Recent years have seen the creation of several new kinds of electronic materials. One example is the discovery of electrical insulators with atomically thin metallic surfaces that are extremely robust to the most common types of impurities and disorder. These new insulators are called topological insulators as the connection between their bulk insulating behavior and surface metallic behavior is described by the branch of mathematics known as topology, which studies properties invariant under continuous changes. More familiar insulators usually have no surface metallic layer, and if they do, it is much less stable to disorder. Another interesting property of the robust surface metallic layer in topological insulators is that the electrons moving in the layer are effectively massless, in that their energy is linearly proportional to their momentum. Electrons in solids exhibit a remarkable variety of collective phenomena including magnetism and superconductivity. Superconductivity is a state of electrons with the signature that resistance to the flow of electric current vanishes at low temperatures. These collective behaviors result from the interactions between electrons. One goal of this project is to understand how topological insulators and related materials, which are currently understood at the level of individual electrons, could lead to new collective phenomena when the interactions between electrons are included. The PI also seeks to understand how new electronic states could be created using interfaces between different materials. Methods used range from advanced techniques originally developed for particle physics to computational simulations, where ideas drawn from the theory of quantum information have had a major impact on our ability to simulate systems in low dimensions. Quantum information generalizes the classical information theory which describes the operation of modern computers and data systems, using ideas specific to quantum systems. One important idea is entanglement, which is a kind of subtle correlation in which the best possible description of a large system does not imply a complete description of its parts. Work on topological order influences many other areas of condensed matter physics and some areas of technology; it contributes to the intellectual foundation for future devices. Several education and outreach efforts will be supported in order to convey to a broad audience the importance and excitement of theoretical materials research.The educational component of this proposal is significant, and the largest expenditure is for graduate student support. This will contribute to the development of a scientifically sophisticated workforce. The PI will carry out new course development and undergraduate student research supervision within the university, in addition to his ordinary teaching load and lectures at advanced schools elsewhere. For outreach beyond the academic community, the PI will expand his lecturing and writing about recent developments and historical highlights of condensed matter physics