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

合作研究：准周期系统中的量子临界性、局域化和动力学

基本信息

批准号：
2103938
负责人：
Sarang Gopalakrishnan
金额：
$ 18万
依托单位：
Pennsylvania State Univ University Park
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-09-01 至 2023-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2103938&HistoricalAwards=false
关键词：
Collaborative Research Quantum Criticality Localization

项目摘要

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.

非技术摘要该项目研究准晶系统中粒子（例如电子）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随机分布）。 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化模式；然而，与晶体不同，这些“准周期”模式不会在空间中重复。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，很大程度上取决于它们是否处于晶体或随机背景。准晶体中的电子表现出更丰富的行为，在磁性和电导率方面具有新型相变。我们还没有一个通用框架来描述这些影响。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。该项目将为研究生和博士后研究员提供国家高度优先领域的技术培训。 PI 将组织一次虚拟研讨会并举办虚拟公开讲座，将准晶体的奇异物理介绍给广泛而多样化的受众。技术摘要该项目旨在开发一个通用框架，用于探索准周期系统中的量子相变、局域化现象和动力学空间调制。考虑到准周期系统在冷原子环境中的重要性、合成金属准晶体的最新进展以及莫尔材料的出现，准周期系统具有很大的实验相关性。这些系统表现出安德森局域化以及非常规磁相等现象。然而，我们对这种物理学的理解受到限制，因为缺乏通用的计算框架，其能力可与描述晶体或随机系统的场论方法相媲美。该项目将使用现实空间技术的组合，以适应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以及半经典方法和基于张量网络的数值方法。要探索的现象包括安德森和多体局域化、磁量子临界性、超流体-绝缘体转变以及准周期势存在下的量子杂质问题。除了培训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将准晶体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价值和更广泛的影响审查标准。

项目成果

期刊论文数量（3）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Many-body localization transition with correlated disorder

具有相关障碍的多体定位转变

DOI：
10.1103/physrevb.106.144201
发表时间：
2022-10
期刊：
Physical Review B
影响因子：
3.7
作者：
Shi, Zhengyan Darius;Khemani, Vedika;Vasseur, Romain;Gopalakrishnan, Sarang
通讯作者：
Gopalakrishnan, Sarang

Aubry-André Anderson model: Magnetic impurities coupled to a fractal spectrum

Aubry-André Anderson 模型：磁性杂质与分形谱的耦合

DOI：
10.1103/physrevb.106.165123
发表时间：
2022-10
期刊：
Physical Review B
影响因子：
3.7
作者：
Wu, Ang;Bauernfeind, Daniel;Cao, Xiaodong;Gopalakrishnan, Sarang;Ingersent, Kevin;Pixley, J. H.
通讯作者：
Pixley, J. H.

Quasiperiodic many-body localization transition in dimension d>1

d>1 维准周期多体局域化转变