Transport in Quantum Spin Systems

该奖项将资助量子物质拓扑相的研究，这是一个涵盖物理学，计算机科学和数学的跨学科研究领域。该领域的一个长期目标是生产具有固有的不受缺陷和噪声影响的特性的新型材料。例如，它们可以携带不会随时间衰减的电流，并且不会在基于其拓扑特性的计算中引入错误，从而优先考虑它们用于构建量子计算机。主要研究人员（PI）将开发一种数学理论，以更好地了解这些材料的特性，特别是如何对它们进行分类以及如何量化它们对缺陷的鲁棒性。参与该项目的学生将与PI一起工作，并获得该领域的专业知识。培养一批精通量子力学的年轻人是量子飞跃的关键部分，该奖项将有助于通过学生的学徒制建立这一人才库。量子霍尔效应是物质拓扑相的主要例子。在没有相互作用的情况下量子霍尔效应的数学理论是在20世纪80年代和90年代发展起来的。近年来，有一个强大的推动力，以发展的工具，在存在的相互作用与潜在的扩展理论的拓扑阶段需要相互作用。该奖项将合并两个突出的方向，在这项研究中，多体定位和多体指数理论。PI的目的是表明，最近构建的指数是强大的多体本地化，无论是作为数学和物理指标，这意味着他们是整数值和常数在每个拓扑阶段，他们保留电导的意义。这项任务需要更好地了解无序多体系统的输运性质比目前可用的。该奖项反映了NSF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。

This award will fund research on topological phases of quantum matter, an interdisciplinary research area encompassing physics, computer science, and mathematics. A longstanding goal of this field is to produce novel materials with properties that are inherently immune to defects and noise. For example, they can carry electrical currents that do not decay in time and do not introduce errors in computations based on their topological properties, prioritizing them for the construction of quantum computers. Primary investigators (PIs) will develop a mathematical theory to understand the properties of such materials better, especially how to classify them and how to quantify their robustness to defects. The students working on the project will work alongside the PIs and gain expertise in the area. Developing a pool of young people proficient in quantum mechanics is a crucial part of quantum leap, and the award will help to build this pool through students' apprenticeships. Integer Quantum Hall effect is the primary example of a topological phase of matter. The mathematical theory of Quantum Hall effect in the absence of interactions was developed in the 1980s and 1990s. In recent years there was a strong push to develop the tools in the presence of interactions with the potential of extending the theory to topological phases requiring interactions. This award will merge two prominent directions in this research, many-body localization, and many-body index theory. PIs aim to show that the recently constructed indices are robust to many-body localization, both as mathematical and physical indices, which means that they are integer valued and constant in each topological phase and that they retain the meaning of electrical conductance. This task requires a better understanding of the transport properties of disordered many-body systems than is currently available. Study of these properties is another focus of the project.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.