Topological and Dynamical Phenomena in Condensed Matter Systems Detected by Quantum Entanglement

量子纠缠检测凝聚态系统中的拓扑和动力学现象

基本信息

批准号：
2001181
负责人：
Shinsei Ryu
金额：
$ 33万
依托单位：
Princeton University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-01-01 至 2023-12-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2001181&HistoricalAwards=false
关键词：
Topological Dynamical Phenomena Condensed Matter

项目摘要

NONTECHNICAL SUMMARYThis award supports theoretical research and education on novel properties of quantum materials and associated phenomena. It has been long recognized that quantum mechanics is essential to understand the basic properties of solids. Understanding the distinction between metals and insulators are one example. With recent advances in experimental techniques, a class of materials has emerged for which subtle quantum effects of the system of their many constituent electrons control macroscopic properties that are characteristic of materials. One example of quantum materials are superconductors. At sufficiently low temperature, a quantum mechanical state forms in which electrons behave collectively leading to conduction of electricity with zero resistance. More recently discovered, is another class of quantum materials that are insulators in their bulk but can support zero resistance conduction of electricity along their surfaces and edges. The metallic surface states in these materials, known as topological insulators, are a consequence of the mathematical structure of the wavefunction which describes the many electron quantum state. The field of mathematics known as topology which focuses on geometric properties of an object that are unchanged by deformations, provides useful ways to describe the structure of the wavefunctions of topological phases in quantum materials. It has become clear that quantum materials can exhibit exotic and surprising properties that do not have a counterpart in ordinary materials. Quantum materials can also host exotic quantum mechanical particles that have intrinsic properties that are quite different from free electrons which make them candidates for the implementation of quantum computers. Novel quantum phenomena can also be found in systems far out of the tranquil state of equilibrium. For example, sufficiently complex quantum many-body systems can "forget" their initial quantum states. In these novel quantum condensed matter systems, quantum entanglement provides a conceptual foundation and tools to study many-body quantum systems. When particles are entangled quantum mechanically, they are connected in a way that affecting one particle will affect all the others, even though they may be separated by vast distances. In this project, the PI aims to develop a deeper theoretical understanding of the properties, including nonequilibrium properties, and phenomena associated with quantum materials, particularly in materials with strongly interacting electrons using concepts such as quantum entanglement together along with others that are associated with the emerging field of quantum information theory. In particular, the PI will examine the nature of the intricate quantum entanglement characteristic of topological phases. He will also investigate how quantum entanglement spreads and propagates in complex many-body quantum systems. A thorough understanding of these problems can pave the way to the discovery of new states of quantum matter and associated phenomena that form the foundations of the next generation of technologies based on quantum mechanics. TECHNICAL SUMMARYThis award supports theoretical research and education with the aim to investigate quantum many-body systems that exhibit novel phenomena, focusing on their topological and far out-of-equilibrium properties. The PI plans to develop a many-body framework to study topological phenomena both in and out of equilibrium, and the structure of multiparty quantum entanglement in topological phases of matter. In particular, the PI plans to construct many-body diagnostics for the topological properties of periodically driven quantum systems in the presence of time-reversal and other symmetries. The PI will seek universal descriptions of quantum information scrambling in complex quantum dynamics using various quantum entanglement measures. To carry out the research, the PI will utilize quantum information theoretical concepts and tools that include quantum entanglement, the channel-state duality, and tensor-networks. The proposed research will lead to a deeper understanding of novel phenomena in quantum many-body systems. The knowledge gained contributes to the foundations of future technological innovations based on quantum mechanical effects. Because of the nature of the proposed work, success in these projects will have impact on many areas of theoretical physics, and may connect to concrete numerical works on model Hamiltonians and experiments in condensed matter systems. Students and young researchers are closely integrated into the research activities and will receive unique training at the frontiers of condensed matter theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

非技术摘要这一奖项支持量子材料和相关现象的新型特性的理论研究和教育。长期以来，人们已经认识到，量子力学对于了解固体的基本特性至关重要。了解金属和绝缘子之间的区别就是一个例子。随着实验技术的最新进展，已经出现了一类材料，其许多构成电子控制宏观特性的微妙量子效应是材料的特征。量子材料的一个例子是超导体。在足够低的温度下，量子机械状态形式，其中电子的行为统称会导致电阻为零的电力传导。最近发现的是另一种类别的量子材料，它们是其大部分的绝缘体，但可以支持沿其表面和边缘的零电阻传导。这些材料中的金属表面状态（称为拓扑绝缘子）是描述许多电子量子状态的波函数的数学结构的结果。被称为拓扑的数学领域，重点是不变变形的物体的几何特性，提供了描述量子材料中拓扑阶段波形的结构的有用方法。很明显，量子材料可以表现出异国情调和令人惊讶的特性，而这些特性没有普通材料的对应物。量子材料还可以容纳具有固有特性的外来量子机械颗粒，这些粒子与自由电子完全不同，这使它们成为量子计算机实施的候选者。新型量子现象也可以在远离平衡状态的系统中找到。例如，足够复杂的量子多体系统可以“忘记”其初始量子状态。在这些新颖的量子凝结物质系统中，量子纠缠提供了研究多体量子系统的概念基础和工具。当粒子机械地纠缠量子时，它们的连接方式会影响一个粒子，即使它们可能被巨大的距离隔开，它们也会影响所有粒子。在该项目中，PI旨在对属性（包括非平衡性能）以及与量子材料相关的现象进行更深入的理论理解，尤其是在具有诸如量子纠缠诸如与量子信息理论的新兴领域相关的其他概念的材料中，尤其是在具有强烈相互作用的电子的材料中。特别是，PI将检查拓扑阶段复杂的量子纠缠特征的性质。他还将研究量子纠缠如何扩散并在复杂的多体量子系统中传播。对这些问题的透彻理解可以为发现新的量子物质状态和相关现象的发现铺平了道路，这些现象构成了基于量子力学的下一代技术的基础。技术摘要这一奖项支持理论研究和教育，目的是研究表现出新现象的量子多体系统，重点是其拓扑和遥不可及的特性。 PI计划开发一个多体框架，以研究均衡的拓扑现象，以及在物质拓扑阶段中多方量子纠缠的结构。特别是，PI计划在存在时间反转和其他对称性的情况下为定期驱动的量子系统的拓扑特性构建多体诊断。 PI将寻求使用各种量子纠缠措施在复杂量子动力学中争夺量子信息的普遍描述。为了进行研究，PI将利用量子信息理论概念和工具，包括量子纠缠，频道状态二元性和张量 - 网络。拟议的研究将导致对量子多体系统中新现象的新现象有更深入的了解。获得的知识为基于量子机械效应的未来技术创新的基础做出了贡献。由于拟议的工作的性质，这些项目的成功将对理论物理的许多领域产生影响，并可能与模型汉密尔顿模型的具体数字作品和凝结物质系统的实验联系起来。学生和年轻的研究人员紧密整合到研究活动中，并将在凝结物质理论的前沿接受独特的培训。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响评估的评估来支持的。