Collaborative Research: Quantum Criticality, Localization and Dynamics in Quasiperiodic Systems

非技术概述本项目研究准晶系统中粒子(如电子)的运动。大多数固体是结晶的(即，它们的原子排列成规则的阵列)或无定形的(即，它们的原子基本上是随机分布的)。上世纪80年代，人们发现了第三种固体，称为准晶。准晶中的原子遵循确定性的结构模式；然而，这些“准周期”模式不同于晶体在空间中的重复。材料中的电子如何移动和相互作用，产生导电性和导热性，以及磁等现象，强烈依赖于它们是在晶体背景中还是在随机背景中。准晶中的电子表现出更丰富的行为，它们的磁性和导电性发生了新的相变。我们还没有一个描述这些影响的总体框架。该项目旨在开发这样一个框架，并将其应用于准周期系统中最近发现的各种现象。该项目将在国家重点领域为研究生和博士后研究员提供技术培训。PIS将组织一个虚拟研讨会并举办虚拟公开讲座，将准晶的奇异物理带给广泛和不同的受众。技术概述本项目旨在开发一个通用框架，用于探索具有准周期空间调制的系统中的量子相变、局域现象和动力学。由于准周期系统在冷原子环境中的重要性，以及在合成金属准晶方面的最新进展，以及云纹材料的出现，准周期系统具有重要的实验意义。这些系统表现出安德森定域化和非常规磁相等现象。然而，我们对这一物理学的理解受到限制，因为缺乏一个普遍适用的计算框架，在功率上可与描述晶体或随机系统的场论方法相媲美。这个项目将使用实空间技术的组合来探索准周期系统中的局域性和量子临界性的物理，以一种适合于准周期势近似重复的独特模式的方式。这些技术包括实空间重整化群方法、半经典方法和基于张量网络的数值方法。要探索的现象包括Anderson和多体局域化，磁量子临界性，超流-绝缘体相变，以及在准周期势存在下的量子杂质问题。除了培养研究生和博士后研究人员外，该项目还将通过虚拟会议和公开演讲的方式将准晶物理学带给更广泛的受众。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 project investigates the motion of particles (such as electrons) in quasicrystalline systems. Most solids are crystalline (i.e., their atoms are arranged in a regular array) or amorphous (i.e., their atoms are distributed essentially randomly). In the 1980s, a third type of solid, called a quasicrystal, was discovered. Atoms in quasicrystals follow deterministic, structured patterns; however, these "quasiperiodic" patterns do not repeat in space unlike those of a crystal.How electrons in a material move and interact, giving rise to electrical and heat conductivity, as well as phenomena like magnetism, depends strongly on whether they are in a crystalline or a random background. Electrons in quasicrystals exhibit even richer behavior, with new classes of phase transitions in their magnetic properties and conductivity. We do not yet have a general framework to describe these effects. This project aims to develop such a framework and apply it to various recently discovered phenomena in quasiperiodic systems.This project will provide technical training to graduate students and a postdoctoral researcher in an area of high national priority. The PIs will organize a virtual symposium and host virtual public lectures to bring the exotic physics of quasicrystals to a broad and diverse audience.Technical summaryThis project aims to develop a general framework for exploring quantum phase transitions, localization phenomena, and dynamics in systems with quasiperiodic spatial modulation. Quasiperiodic systems are of great experimental relevance, given their importance in cold-atom settings and recent advances in synthesizing metallic quasicrystals, as well as the advent of Moire materials. These systems exhibit phenomena such as Anderson localization as well as unconventional magnetic phases. However, our understanding of this physics is limited by the lack of a generally applicable computational framework, comparable in power to the field-theoretic methods that describe crystalline or random systems.This project will explore the physics of localization and quantum criticality in quasiperiodic systems using a combination of real-space techniques, in a way that is tailored to the unique patterns of approximate repetitions of quasiperiodic potentials. The techniques include real-space renormalization-group methods as well as semiclassical methods and tensor-network-based numerics. The phenomena to be explored include Anderson and many-body localization, magnetic quantum criticality, superfluid-insulator transitions, and quantum impurity problems in the presence of quasiperiodic potentials. In addition to training graduate students and a postdoctoral researcher, this project will bring the physics of quasicrystals to a broader audience by means of a virtual conference and public lectures.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.