Topological order and Anyons in and out of Equilibrium

拓扑序和平衡态内外的任意子

• 批准号: 2220703
• 负责人: Ashvin Vishwanath
• 金额: $ 56万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2220703&HistoricalAwards=false
• 关键词: Topological; order; Anyons; out; Equilibrium

NONTECHNICAL SUMMARYThis award supports theoretical research into the quantum physics of many interacting particles, often referred to as quantum matter. These systems are the gateway to a rich and promising scientific arena, given the extraordinary ability of quantum particles to remain tied to one another even when separated, a property termed quantum entanglement. Realizations of quantum matter are everywhere, ranging from electrons in crystals to engineered platforms consisting of arrays of atoms. In this project, the PI and his team will explore strategies to create highly entangled quantum matter and to identify the features that characterize them. A particularly interesting subclass is topological matter, in which new excitations called "anyons" arise that are entirely distinct from the individual components that go into building them. Such excitations are speculated to lead to novel material properties and capabilities in quantum information. The PI will explore new arenas to realize topological states, including in artificial materials created by stacking atomically thin sheets and by driving matter with external fields far from thermal equilibrium. The education of the next generation of junior scientists is a key part of this project. Undergraduate and graduate students will be exposed to modern ideas of quantum condensed matter physics through coursework as well as research collaborations. This will contribute to the US workforce in fundamental science and quantum technologies. The research outcomes and course materials developed throughout the course of this project will be widely disseminated via non-technical summaries, pedagogical lecture notes, as well as seminars, colloquia and lecture series at scientific schools for young researchers.TECHNICAL SUMMARYThis award supports theoretical research on quantum states of matter with novel excitations stabilized by topology, to identify their experimental signatures and to enable their realizations in solids and ultracold quantum gases. While a glimpse of topological order and the associated anyon excitations have previously appeared in the fractional quantum Hall effect, this award will focus on realizing these and other topological states in a wider set of systems and in the absence of strong magnetic fields. The topological character of these states make their detection a challenge. The PI will study models of electronic and cold atom systems that are both promising platforms for topological orders and allow for measurements that can unequivocally point to their realization. Moving beyond ground states, driven systems harboring anyon excitations exhibit an extra layer of complexity and richness, and furnish an alternate route to stabilizing topological orders. The PI will explore topological orders driven far from equilibrium, due to external drives and/or measurements as well as out-of-equilibrium routes to realizing new states, including ones with non-Abelian anyon excitations.This award also supports the training of the next generation of researchers in modern theoretical physics, via research and coursework. New course material at the graduate level will be developed, which will incorporate insights gleaned from research. The research outcomes and course materials developed throughout the course of this project will be widely disseminated via non-technical summaries, pedagogical lecture notes, as well as seminars, colloquia and lecture series at scientific schools for young researchers.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.

非技术总结该奖项支持对许多相互作用的粒子的量子物理的理论研究，这些粒子通常被称为量子物质。这些系统是通往一个丰富而有前途的科学舞台的门户，因为量子粒子即使分开也能保持相互联系的非凡能力，这种特性被称为量子纠缠。量子物质的实现无处不在，从晶体中的电子到由原子阵列组成的工程平台。在这个项目中，PI和他的团队将探索创造高度纠缠的量子物质的策略，并确定它们的特征。一个特别有趣的子类是拓扑物质，在这种物质中，新的激子出现，称为“任意子”，与构成它们的各个组成部分完全不同。据推测，这种激发导致了量子信息中新的材料性质和能力。PI将探索实现拓扑状态的新领域，包括通过原子堆叠薄片创建的人造材料，以及通过远离热平衡的外场驱动物质。下一代初级科学家的教育是这一项目的关键部分。本科生和研究生将通过课程学习和研究合作接触到量子凝聚态物理的现代思想。这将为美国基础科学和量子技术领域的劳动力做出贡献。在整个项目过程中开发的研究成果和课程材料将通过非技术性摘要、教学讲稿以及面向年轻研究人员的科学学校的研讨会、座谈会和系列讲座来广泛传播。技术总结该奖项支持对具有通过拓扑稳定的新激发的物质的量子态的理论研究，以确定其实验特征，并使其能够在固体和超冷量子气体中实现。虽然之前在分数量子霍尔效应中已经出现过拓扑有序和相关的任意子激发的一瞥，但本次奖项将专注于在更广泛的系统中以及在没有强磁场的情况下实现这些和其他拓扑态。这些状态的拓扑特性使得它们的检测成为一个挑战。PI将研究电子和冷原子系统的模型，这些模型都是拓扑有序的有希望的平台，并允许测量明确地指向它们的实现。除了基态之外，含有任意子激发的驱动系统显示出额外的一层复杂性和丰富性，并为稳定拓扑秩序提供了另一条途径。PI将探索由于外部驱动和/或测量而导致的远离平衡的拓扑序，以及实现新状态的非平衡路径，包括具有非阿贝尔任意子激发的状态。该奖项还通过研究和课程工作支持现代理论物理中的下一代研究人员的培训。将开发研究生水平的新课程材料，其中将纳入从研究中收集的见解。在整个项目过程中开发的研究成果和课程材料将通过非技术性摘要、教学讲稿以及科学学校为年轻研究人员举办的研讨会、座谈会和系列讲座来广泛传播。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进行评估，被认为值得支持。

项目成果

Many-body ground states from decomposition of ideal higher Chern bands: Applications to chirally twisted graphene multilayers

• DOI: 10.1103/physrevresearch.5.023166
• 发表时间: 2023-06-01
• 期刊: PHYSICAL REVIEW RESEARCH
• 影响因子: 4.2
• 作者: Dong, Junkai;Ledwith, Patrick J.;Vishwanath, Ashvin
• 通讯作者: Vishwanath, Ashvin

XY* Transition and Extraordinary Boundary Criticality from Fractional Exciton Condensation in Quantum Hall Bilayer

量子霍尔双层中分数激子凝聚的 XY* 跃迁和非凡边界临界点

• DOI: 10.1103/physrevx.13.031023
• 发表时间: 2023
• 期刊: Physical Review X
• 影响因子: 12.5
• 作者: Zhang, Ya-Hui;Zhu, Zheng;Vishwanath, Ashvin
• 通讯作者: Vishwanath, Ashvin