Understanding spectral statistics and dynamics in strongly-interacting quantum many-body systems

了解强相互作用量子多体系统中的光谱统计和动力学

• 批准号: EP/X042812/1
• 负责人: Amos Chan
• 金额: $ 174.8万
• 依托单位: Lancaster University
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX042812%2F1
• 关键词: Understanding; spectral; statistics; dynamics; strongly

The dynamics of quantum many-body systems is a fundamental yet notoriously difficult subject due to the nature of strong interactions between macroscopic number of constituents in the systems. Consider setting up a many-body system in a "simple" quantum state, one that does not have much non-local correlation between different subsystems. What are the fates of the system as it evolves in time? Does the system thermalize and exhibit chaotic behaviour, or does it localize and retain information of its initial state?A simple and elegant way of tackling these questions is to investigate the spectral statistics of the quantum many-body systems. A physical system can often be represented by a Hamiltonian - a matrix with a spectrum of energy levels which the system can occupy. The study of spectral statistics asks, what generic features does the correlation among the energy levels in the spectrum capture? Spectral statistics is a fundamental subject in physics due to its role as a robust diagnostic of quantum chaos, and due to universality - generic systems exhibit identical spectral statistics depending only on symmetry classes and dimensionality. In the last five years, spectral statistics has been utilized in multiple frontiers of modern physics, including the demonstration that black holes behave like random matrices in sufficiently late time; a debate concerning the existence of an important dynamical phase called the many-body localization; and the discovery of universal spectral signatures in quantum many-body chaotic systems, as described below.A recent discovery shows that the spectrum of generic quantum many-body chaotic systems has an extended region in which the spectral correlation deviates from known behaviour derived from random matrices. This region grows as the system size increases, and therefore presents a significant gap in our understanding of spectral statistics in the presence of many-body interaction. How does the existence of anomalous spectral correlation affect the scrambling of quantum information? This proposal aims to address such a question, and analytically extract novel signatures of spectral statistics and dynamics in isolated and open quantum many-body systems. Furthermore, despite its importance, spectral statistics in quantum many-body systems has not been experimentally measured, owing to the difficulties of resolving the tight spacing in the spectrum. The second aim of this fellowship is to experimentally measure, in collaboration with experimentalist partners, key signatures of spectral statistics in quantum many-body simulators in the lab for the first time.This project is especially timely, as it deepens and sharpens the understanding of the roles of many-body interaction in the information scrambling and processing in quantum systems, responding to the recent revival in quantum chaos, and to the rapid developments in quantum simulations of quantum many-body systems. Achieving these goals will deliver significant impacts in the constructions of broadly applicable analytical frameworks; in the first experimental measurement of spectral statistics in quantum many-body simulators; and in establishing new connections between communities in condensed matter, quantum information, and high energy physics.

量子多体系统的动力学是一个基本但众所周知的困难，这是由于系统中宏观数量的成分数量之间的强烈相互作用的性质。考虑在“简单”量子状态下设置多体系统，该系统在不同子系统之间没有太多非本地相关性。随着时间的流逝，系统的命运是什么？该系统是否会热力和表现出混乱的行为，或者它本地化并保留其初始状态的信息？解决这些问题的一种简单而优雅的方法是研究量子多体系统的光谱统计。物理系统通常可以用哈密顿量来表示，这是一个具有能量水平的矩阵，系统可以占据。光谱统计数据的研究询问，光谱捕获中能量水平之间的相关性有什么通用特征？光谱统计是物理学的基本主题，因为它是量子混乱的强大诊断，并且由于普遍性 - 通用系统仅根据对称类别和维度表现出相同的光谱统计。在过去的五年中，光谱统计数据被用于现代物理学的多个边界，包括证明黑洞在足够晚的时间内表现得像随机矩阵。关于存在称为多体定位的重要动力学阶段存在的辩论。如下所述，量子多体混沌系统中通用光谱特征的发现。最近的发现表明，通用量子多体混沌系统的光谱具有扩展区域，其中光谱相关性与从随机矩阵得出的已知行为偏离。随着系统大小的增加，该区域的生长，因此在存在多体相互作用的情况下对光谱统计的理解构成了显着差距。异常光谱相关的存在如何影响量子信息的争夺？该提案旨在解决这个问题，并在分析和开放的量子多体系统中分析地提取光谱统计和动力学的新型标志。此外，尽管其重要性，但由于解决光谱中的紧密间距的困难，量子多体系统中的光谱统计量尚未进行实验测量。 The second aim of this fellowship is to experimentally measure, in collaboration with experimentalist partners, key signatures of spectral statistics in quantum many-body simulators in the lab for the first time.This project is especially timely, as it deepens and sharpens the understanding of the roles of many-body interaction in the information scrambling and processing in quantum systems, responding to the recent revival in quantum chaos, and to the rapid developments in quantum simulations of量子多体系统。实现这些目标将对广泛适用的分析框架的构建产生重大影响；在量子多体模拟器中光谱统计的第一个实验测量中；并在凝结物质，量子信息和高能量物理学中建立社区之间的新联系。