Universality and topology in gapless systems and far from equilibrium

用于电子设备的材料有许多微观缺陷、缺陷和其他样品到样品的变化。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。普遍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通用标度定律，例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，它们显示出精确量化的电和热输运属性，这些属性与急剧量化的拓扑不变量有关。在过去的十年里，固体物理、量子场论、量子信息论和形式数学的思想的显著融合已经产生了一个基本完整的理论框架，用于理解和表征低温热平衡绝缘或超导(带隙)物质中的这种拓扑相。这些理论进展反过来又推动了许多新的拓扑绝缘和超导材料的发现，导致了对基本数学思想的美丽实验证实，并为在微电子、光学和量子信息处理设备中利用它们的强大性能打开了大门。这项拟议研究的主要目标是扩大对宇宙拓扑相和相变的系统理解，这些相变出现在：i)由于依赖时间的强迫而远远偏离热平衡的固态设备，ii)在新兴量子计算处理器中发现的嘈杂的量子电路动力学，以及iii)凝聚态物理长期谜团背后的物质的导电(无间隙)相，例如起源高温超导和奇怪的金属行为。这项工作将解决有关自然界中可能出现的物质的量子相的类型，以及使用噪声和不完美的量子系统进行量子计算的基本能力和限制的基本问题。反过来，这种理解将被用来设计稳健的方法，以动态控制电子设备和量子计算机中的关联和纠缠，这些设备和量子计算机对控制误差和其他噪声和缺陷来源不敏感，这些噪声和缺陷构成了当前量子技术的关键瓶颈。

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.