Novel Topological States in Correlated Quantum Systems

非技术总结该奖项支持在理解固态材料中物质的新量子态方面的理论研究和教育。在低温下，量子力学可以将材料带入没有经典类似物的物质状态。物质的拓扑态是物质的一种新的量子态，它们表现出惊人的新的物理性质。例如，某些拓扑态中的载流子行为就像是一个电子的一小部分，它们的性质可以被用来构建健壮的量子计算机。研究活动的主要内容包括：1)开发一个新的理论框架来系统地理解拓扑态，并开发新的计算技术来可靠地模拟这些态。2)应用这些技术研究真实材料中的拓扑态及其物理性质。3)开发有助于在材料中寻找新的拓扑态的指导原则。该项目将产生量子材料科学和量子技术进步所需的知识和计算方法。教育活动包括为本科生和研究生开发教学课程、讲座和期刊俱乐部系列，重点是现代凝聚态物理学中发现的物质的新状态。作为一项推广活动，将创建一个互动网站来传播教材和演示拓扑现象，目的是激发人们对科学和技术的普遍兴趣。技术总结该奖项支持在理解物质的拓扑量子态方面的理论研究和教育。理论上已经预测了非常丰富的关联驱动的拓扑相的种类；然而，在实际材料中只证实了其中的少数几个的存在。相关的挑战是现有的关联量子系统的理论和数值方法的局限性，以及缺乏物理指导原则来指导寻找许多关联的拓扑态。这一项目解决了这两个挑战。研究活动包括三个主要方面：1)PI将进一步开发一个对称张量网络框架和适用于研究相关拓扑相的数值算法。张量网络可以被视为一种新的量子多体物理语言，能够捕捉量子态的拓扑性质。2)通过应用该框架，PI将搜索实现关联驱动的拓扑相的模型系统，包括相关过渡金属材料的模型。此外，还将计算候选拓扑材料的激发性质，并与实验进行比较。3)PI将发展与微观细节无关的基于对称性的指导原则，帮助寻找材料中的拓扑态。这项研究与量子信息科学和数学中的代数拓扑学密切相关，可以为这些学科带来新的见解。教育活动包括为本科生和研究生开发教学课程、讲座和期刊俱乐部系列，重点是现代凝聚态物理学中发现的物质的新状态。PI将开发和维护一个互动网站，托管研究和教学材料，其中将包括凝聚态物理和张量网络中的拓扑现象的演示。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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 in understanding novel quantum states of matter in solid-state materials. At low temperatures, quantum mechanics can bring materials into states of matter that have no classical analog. Topological states of matter are such novel quantum states of matter, and they exhibit striking new physical properties. For example, charge carriers in some topological states behave as if they were a fraction of an electron, and their properties can be exploited to build robust quantum computers.The thrusts of the research activities include: 1) Developing a new theoretical framework to systematically understand topological states and developing new computational techniques to simulate these states in a reliable fashion. 2) Applying these techniques to investigate topological states and their physical properties in real materials. 3) Developing guiding principles helpful in searching for new topological states in materials.This project will generate knowledge and computational methods needed for advances in quantum material science and quantum technology. The educational activities include developing pedagogical courses, lectures, and journal-club series for undergraduate and graduate students, with emphasis on the new states of matter discovered in modern condensed matter physics. As an outreach activity, an interactive website will be created to disseminate teaching materials and to demonstrate topological phenomena, with the aim of sparking general interest in science and technology.TECHNICAL SUMMARYThis award supports theoretical research and education in understanding topological quantum states of matter. Very rich classes of correlation-driven topological phases have been predicted theoretically; however, the existence of only few of them has been confirmed in real materials. The relevant challenges are the limitations of currently available theoretical and numerical methods for correlated quantum systems, as well as the lack of physical guiding principles to direct the search for many correlated topological states. This project addresses both these challenges.The research activities comprise three main thrusts: 1) The PI will further develop a symmetric tensor network framework and numerical algorithms suitable for investigating correlated topological phases. The tensor network can be viewed as a new language for quantum many-body physics capable of capturing topological properties of quantum states. 2) By applying this framework, the PI will search for model systems that realize correlation-driven topological phases, including models for correlated transition-metal materials. In addition, excitation properties of candidate topological materials will be computed and compared with experiments. 3) The PI will develop symmetry-based guiding principles that are independent of microscopic details, aiding the search for topological states in materials.The research is closely connected to quantum information science and algebraic topology in mathematics, and it could bring new insight in these disciplines. The educational activities include developing pedagogical courses, lectures, and journal-club series for undergraduate and graduate students, with emphasis on the new states of matter discovered in modern condensed matter physics. The PI will develop and maintain an interactive website hosting research and teaching materials, which will include demonstrations of topological phenomena in condensed matter physics and tensor networks.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.