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.

由于系统中宏观数量的成分之间存在强相互作用的性质，量子多体系统的动力学是一个基础但又非常困难的课题。考虑在“简单”量子态下建立一个多体系统，该系统在不同子系统之间没有太多非局部相关性。随着时间的推移，系统的命运会如何？系统是否热化并表现出混沌行为，或者是否局部化并保留其初始状态的信息？解决这些问题的一个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——一个具有系统可以占据的能级谱的矩阵。光谱统计研究提出的问题是，光谱中能级之间的相关性捕获了哪些一般特征？光谱统计是物理学中的一个基础学科，因为它作为量子混沌的稳健诊断，并且由于普遍性——通用系统仅依赖于对称性类别和维度而表现出相同的光谱统计。在过去的五年中，光谱统计已被用于现代物理学的多个前沿领域，包括证明黑洞在足够晚的时间里表现得像随机矩阵；关于称为多体定位的重要动力学阶段是否存在的争论；以及量子多体混沌系统中通用光谱特征的发现，如下所述。最近的一项发现表明，通用量子多体混沌系统的光谱具有一个扩展区域，其中光谱相关性偏离源自随机的已知行为矩阵。该区域随着系统规模的增加而增长，因此在多体相互作用的情况下，我们对光谱统计的理解存在显着差距。反常谱相关性的存在如何影响量子信息的置乱？该提案旨在解决这样的问题，并分析提取孤立和开放量子多体系统中光谱统计和动力学的新特征。此外，尽管量子多体系统中的光谱统计很重要，但由于难以解决光谱中的紧密间距，因此尚未通过实验测量。该奖学金的第二个目标是与实验伙伴合作，首次在实验室中通过实验测量量子多体模拟器中光谱统计的关键特征。这个项目特别及时，因为它加深和加深了对多体相互作用在量子系统信息加扰和处理中的作用，响应最近量子混沌的复兴，以及量子多体系统量子模拟的快速发展。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；量子多体模拟器中光谱统计的首次实验测量；并在凝聚态物质、量子信息和高能物理领域之间建立新的联系。