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

该奖项支持关于量子材料和相关现象的新特性的理论研究和教育。人们早就认识到量子力学对于理解固体的基本性质是必不可少的。理解金属和绝缘体之间的区别就是一个例子。随着实验技术的最新进展，出现了一类材料，它们的许多组成电子系统的微妙量子效应控制着材料的宏观特性。量子材料的一个例子是超导体。在足够低的温度下，形成一种量子力学状态，其中电子集体行为导致零电阻导电。最近发现的另一类量子材料是绝缘体，但可以支持沿其表面和边缘的零电阻导电。这些材料中的金属表面状态，被称为拓扑绝缘体，是描述许多电子量子态的波函数的数学结构的结果。被称为拓扑学的数学领域关注的是物体不受变形影响的几何特性，它为描述量子材料中拓扑相的波函数结构提供了有用的方法。很明显，量子材料可以表现出在普通材料中没有的奇异和令人惊讶的特性。量子材料也可以承载奇异的量子力学粒子，这些粒子具有与自由电子完全不同的内在特性，这使它们成为实现量子计算机的候选者。在远离平静平衡状态的系统中也可以发现新的量子现象。例如，足够复杂的量子多体系统可以“忘记”它们的初始量子态。在这些新型量子凝聚态系统中，量子纠缠为研究多体量子系统提供了概念基础和工具。当粒子以量子力学的方式纠缠在一起时，它们以一种影响一个粒子会影响所有其他粒子的方式连接在一起，即使它们可能相隔很远。在这个项目中，PI的目标是对量子材料的特性，包括非平衡特性和与量子材料相关的现象，特别是在具有强相互作用电子的材料中，使用量子纠缠等概念，以及与量子信息理论新兴领域相关的其他概念，进行更深入的理论理解。特别是，PI将研究拓扑相的复杂量子纠缠特性的本质。他还将研究量子纠缠如何在复杂的多体量子系统中传播和传播。对这些问题的透彻理解可以为发现量子物质的新状态和相关现象铺平道路，这些现象构成了基于量子力学的下一代技术的基础。该奖项支持理论研究和教育，旨在研究表现出新现象的量子多体系统，重点关注它们的拓扑和远非平衡特性。PI计划开发一个多体框架来研究平衡内外的拓扑现象，以及物质拓扑相中的多方量子纠缠结构。特别是，PI计划在存在时间反转和其他对称性的情况下，为周期驱动量子系统的拓扑特性构建多体诊断。PI将使用各种量子纠缠措施寻求复杂量子动力学中量子信息混乱的通用描述。为了开展这项研究，PI将利用量子信息理论概念和工具，包括量子纠缠，通道状态对偶性和张量网络。所提出的研究将导致对量子多体系统中新现象的更深层次的理解。所获得的知识有助于基于量子力学效应的未来技术创新的基础。由于所提出的工作的性质，这些项目的成功将对理论物理的许多领域产生影响，并可能与模型哈密顿量和凝聚态系统实验的具体数值工作联系起来。学生和年轻的研究人员紧密地融入到研究活动中，并将在凝聚态理论的前沿接受独特的培训。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.