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

非技术性概述本项目研究准晶体系统中粒子（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阵列）或无定形（即，它们的原子基本上是随机分布的）。在20世纪80年代，人们发现了第三种固体，称为准晶体。准晶体中的原子遵循确定性的结构模式;然而，这些“准周期”模式不像晶体那样在空间中重复。材料中的电子如何移动和相互作用，从而产生导电性和导热性，以及磁性等现象，在很大程度上取决于它们是在晶体还是随机背景中。准晶体中的电子表现出更丰富的行为，在它们的磁性和导电性中具有新的相变类型。我们还没有一个总体框架来描述这些影响。该项目旨在制定这样一个框架，并将其应用于最近发现的准周期系统中的各种现象，该项目将在国家高度优先领域向研究生和博士后研究人员提供技术培训。PI将组织一个虚拟的研讨会，并举办虚拟的公开讲座，把准晶体的异国情调的物理学，以广泛和多样化的观众。技术摘要本项目旨在开发一个通用的框架，探索量子相变，局域化现象，和动力学系统与准周期空间调制。准周期系统具有很大的实验相关性，因为它们在冷原子环境中的重要性和最近在合成金属准晶方面的进展，以及莫尔材料的出现。这些系统表现出的现象，如安德森本地化以及非常规的磁相。然而，我们对这一物理学的理解是有限的，缺乏一个普遍适用的计算框架，在权力相媲美的场论方法，描述晶体或随机系统。这个项目将探讨物理的局域化和量子临界准周期系统使用的组合实空间技术，在一种方式，是针对准周期电位的近似重复的独特模式。这些技术包括实空间重整化群方法以及半经典方法和基于张量网络的数值方法。要探讨的现象包括安德森和多体局域化，磁量子临界，超流绝缘体的转变，和量子杂质问题的准周期电位的存在。除了培养研究生和博士后研究员外，该项目还将通过虚拟会议和公开讲座的方式向更广泛的受众介绍准晶体物理学。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。

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.