Universality and topology in gapless systems and far from equilibrium

无间隙系统中的普遍性和拓扑结构且远离平衡

• 批准号: RGPIN-2022-03585
• 负责人: Potter, Andrew
• 金额: $ 2.84万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=763069
• 关键词: Universality; topology; gapless; systems; far

Materials used for electronic devices have many microscopic imperfections, defects, and other sample-to-sample variations. Despite this, at macroscopic scales, the collective properties of many electrons at very low temperatures display striking "universal" behaviors that are remarkably insensitive to these complicated microscopic details. Dramatic examples of universal quantum phenomena include universal scaling laws for how thermodynamic and transport properties depend on control-knobs such as frequency, temperature and field-strength near quantum phase transitions, and topological phases of matter such as quantum Hall fluids and topological insulators that exhibit precisely quantized electrical and thermal transport properties tied to sharply-quantized topological invariants. In the past decade, a remarkable confluence of ideas from solid-state physics, quantum field theory, quantum information theory, and formal mathematics have produced an essentially complete theoretical framework for understanding and characterizing such topological phases in insulating or superconducting (gapped) matter in thermal equilibrium at low-temperature. These theoretical advances have, in turn, driven materials discovery of many new topological insulating and superconducting materials, leading to beautiful experimental confirmations of fundamental mathematical ideas, and opening the door to harnessing their robust properties in microelectronic, optical, and quantum information processing devices. The main goal of the proposed research is to extend this systematic understanding of universal topological phases and phase transitions that arise in i) solid-state devices driven far out of thermal equilibrium by time-dependent forcing, ii) noisy quantum circuit dynamics found in emerging quantum computing processors, and iii) conducting (gapless) phases of matter underlying longstanding mysteries of condensed matter physics such as the origins high-temperature superconductivity and strange metal behavior. This work will address fundamental questions about both the types of quantum phases of matter that can arise in nature, and the fundamental capabilities and limitations of using noisy and imperfect quantum systems for quantum computation. This understanding will, in turn, be used to design robust methods to dynamically control the correlations and entanglement in electronic devices and quantum computers that are insensitive to control errors and other sources of noise and imperfections that form key bottlenecks for current quantum technology.

用于电子设备的材料具有许多微观缺陷、缺陷和其他样品间变化。尽管如此，在宏观尺度上，许多电子在极低温度下的集体性质显示出惊人的“普遍”行为，对这些复杂的微观细节非常不敏感。普适量子现象的戏剧性例子包括热力学和输运性质如何依赖于控制旋钮的普适标度律，如量子相变附近的频率，温度和场强，以及物质的拓扑相，如量子霍尔流体和拓扑绝缘体，它们表现出精确量化的电和热输运性质，与sharp量子化拓扑不变量联系在一起。在过去的十年中，固态物理学、量子场论、量子信息论和形式数学的思想显著融合，产生了一个基本上完整的理论框架，用于理解和表征低温热平衡下绝缘或超导（带隙）物质中的拓扑相。这些理论上的进步反过来又推动了许多新的拓扑绝缘和超导材料的发现，导致基本数学思想的美丽实验证实，并打开了在微电子，光学和量子信息处理设备中利用其强大特性的大门。拟议研究的主要目标是扩展对普遍拓扑相位和相变的系统理解，这些相位和相变出现在i）由时间相关强迫驱动的远离热平衡的固态设备，ii）新兴量子计算处理器中发现的噪声量子电路动力学，以及iii）传导（无间隙）物质相，这是凝聚态物理学长期存在的谜团的基础，例如高-温度超导性和奇异金属行为。这项工作将解决有关自然界中可能出现的物质量子相类型的基本问题，以及使用噪声和不完美量子系统进行量子计算的基本能力和局限性。反过来，这种理解将用于设计鲁棒的方法，以动态控制电子设备和量子计算机中的相关性和纠缠，这些方法对控制误差和其他噪声源和缺陷不敏感，这些噪声和缺陷构成了当前量子技术的关键瓶颈。