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的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上创建拓扑状态，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。第二个研究领域是数值矩阵积态方法和解析理论的结合如何导致对低维强相关物理中一些具有挑战性的问题的见解。本项目的两个目标是理解相互作用无序系统中多体定位的一维模型，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。本节建立在理解量子信息理论概念（如纠缠）如何有助于相关材料的数值模拟的先前工作的基础上。这项提案的教育部分是重要的，最大的支出是研究生的支持。这将有助于发展一支科学熟练的劳动力队伍。除了日常的教学工作和在其他先进学校的讲座外，PI还将在大学内开展新课程开发和本科生研究监督。为了拓展到学术界之外，PI将扩大他关于凝聚态物理的最新发展和历史亮点的演讲和写作。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型电子材料。一个例子是发现了具有原子级薄金属表面的电绝缘体，这种绝缘体对最常见的杂质和无序类型非常坚固。这些新型绝缘体被称为拓扑绝缘体，因为它们的整体绝缘行为和表面金属行为之间的联系被称为拓扑数学分支，它研究连续变化下的不变性。更常见的绝缘体通常没有表面金属层，即使有，对无序的稳定性也差得多。拓扑绝缘体中坚固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。超导是电子的一种状态，其特征是在低温下对电流流动的阻力消失。这些集体行为源于电子之间的相互作用。该项目的一个目标是了解拓扑绝缘体和相关材料，目前在单个电子水平上被理解，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来创建新的电子状态。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提取的思想对我们模拟低维系统的能力产生了重大影响。量子信息运用量子系统特有的思想，概括了描述现代计算机和数据系统运行的经典信息理论。一个重要的概念是纠缠，它是一种微妙的关联，在这种关联中，对一个大系统的最佳描述并不意味着对其各部分的完整描述。拓扑秩序的研究影响了凝聚态物理的许多其他领域和一些技术领域；它有助于为未来的设备奠定智力基础。为了向广大读者传达理论材料研究的重要性和兴奋性，将支持若干教育和推广工作。这项提案的教育部分是重要的，最大的支出是研究生的支持。这将有助于发展一支科学熟练的劳动力队伍。除了日常的教学工作和在其他先进学校的讲座外，PI还将在大学内开展新课程开发和本科生研究监督。为了拓展到学术界之外，PI将扩大他关于凝聚态物理的最新发展和历史亮点的演讲和写作

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