Entanglement and emergence in new quantum states of matter

非技术总结这个奖项支持理论研究和教育到新的阶段的物质，称为拓扑阶段。正如朗道发现的那样，通过了解在保持不变的情况下，可以对给定的状态进行什么样的对称变换，可以组织液体和晶体等物质的状态。例如，围绕普通盐晶体的主轴旋转90度，将新原子旋转到最初由同一种原子占据的位置，因此晶体看起来没有变化。对称性的概念也允许磁性和其他状态通过类似的考虑来组织。 近年来，人们发现来自拓扑学的思想，即数学的分支，涉及物体的几何性质不会因变形、扭曲和拉伸而改变，使人们深入了解了物质的新的可能相，称为拓扑相。其中拓扑绝缘体与普通绝缘体有着本质的不同，虽然其本体不导电，但其表面却导电，就好像它们属于金属一样。该奖项支持将利用金属表面态等拓扑现象来发展拓扑相系统理论的理论研究。量子纠缠预计将在这一理论中发挥至关重要的作用，这将使搜索，发现和设计新的拓扑状态。量子纠缠是指一个系统的各个组成部分的状态，即使这些组成部分在空间上相隔很远，也不能相互独立地描述的现象;作为量子力学的结果，各个组成部分以相关的方式起作用。拓扑量子纠缠导致可能的惊人现象，包括电荷是电子电荷的一小部分，粒子，在一个基本的意义上是介于电子和光子-量子的光，和一个更统一的理解的起源光和电子。新的拓扑状态可以被发现或设计，可以形成利用量子力学状态的操作的计算的基础，拓扑量子计算机。技术概要该奖项支持理论研究和教育，旨在发现新的理论概念和方法，以更精确地发展拓扑相位和对称性保护拓扑（SPT）相位的综合理论。本研究分为四个部分：（1）开发标记拓扑/SPT相的系统;（2）发现可以测量和区分不同拓扑相的一组物理测量;（3）创建允许对所有拓扑相进行分类的数学理论;（4）开发有效的方法以使得能够计算包含拓扑/SPT相的通用系统的相图。这项研究可能导致发现一类新的量子材料，高度纠缠的拓扑材料，这可能为一类新的设备概念以及通过利用量子纠缠而成为可能的电子和光学设备提供基础。该理论的发展可能需要或刺激新数学的创造，并可能导致从量子计算到基本粒子等领域的基本见解。

NONTECHNICAL SUMMARYThis award supports theoretical research and education into new phases of matter, called topological phases. As Landau discovered, states of matter such as liquids and crystals can be organized through understanding what symmetry transformations can be performed on a given state that leaves it unchanged. For example, a rotation of 90 degrees around a principle axis of a crystal of common salt, rotates new atoms into positions that were originally occupied by the very same kind of atom, so the crystal appears unchanged. The concept of symmetry also allows magnetic and other states to be organized by similar considerations. In recent years, it has been discovered that ideas from topology, the branch of mathematics concerned with geometric properties that are unchanged by deformations, twisting, and stretching objects, brings insight into new possible phases of matter, called topological phases. Among these are topological insulators that are fundamentally different from ordinary insulators in that while the bulk does not conduct electricity, their surfaces do, as if they belonged to a metal.This award supports theoretical research that will use topological phenomena like the metallic surface states to develop a systematic theory of topological phases. Quantum entanglement is expected to play a crucial role in this theory which will enable the search, discovery, and design of new topological states. Quantum entanglement refers to the phenomenon whereby states of individual components of a system, eventhough the components may be spatially separated by large distances, cannot be described independently of each other; as a consequence of quantum mechanics, the individual components act in a correlated way.Topological quantum entanglement leads to possible amazing phenomena, including electric charge that is a fraction of an electron charge, particles that are in a fundamental sense between electrons and photons - the quantum of light, and a more unified understanding of the origin of light and electrons. New topological states may be discovered or designed that can form the foundations for computation that utilizes the manipulation of quantum mechanical states, a topological quantum computer.TECHNICAL SUMMARY This award supports theoretical research and education with the aim of discovering new theoretical concepts and methods to more precisely develop a comprehensive theory of topological phases and symmetry protected topological (SPT) phases. The research has 4 parts: (1) develop a system to label topological /SPT phases; (2) discover a set of physical measurements that can measure and distinguish different topological phases; (3) create a mathematical theory that allows for the classification of all topological phases; (4) develop effective methods to enable the calculation of the phase diagram of a generic system that contains topological/SPT phases. This research may lead to the discovery of a new class of quantum materials, highly entangled topological materials, which may provide the foundations for a new class of device concepts and electronic and optical devices made possible by exploiting quantum entanglement. The development of the theory may require or stimulate the creation of new mathematics and may lead to fundamental insights into areas extending from quantum computing to elementary particles.