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的，但众所周知的困难的问题，由于在系统中的宏观数量的组分之间的强相互作用的性质。考虑在一个“简单”量子态中建立一个多体系统，这个量子态在不同的子系统之间没有太多的非定域相关性。随着时间的推移，系统的命运是什么？系统是否会热化并表现出混沌行为，或者它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。一个物理系统通常可以用一个哈密顿量来表示--一个具有系统可以占据的能级谱的矩阵。光谱统计学的研究会问，光谱中能级之间的相关性捕获了什么一般特征？光谱统计是物理学中的一个基本课题，因为它是量子混沌的强大诊断，并且由于普适性-通用系统仅依赖于对称类和维度表现出相同的光谱统计。在过去的五年中，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内表现得像随机矩阵;关于一个重要的动力学阶段（称为多体局域化）存在的争论;以及量子多体混沌系统中普遍光谱特征的发现，如下所述，最近的发现表明，一般的量子多体混沌系统的谱具有扩展区域，其中谱相关偏离从随机矩阵导出的已知行为。该区域随着系统尺寸的增加而增长，因此在我们对多体相互作用存在下的光谱统计的理解中存在显著的差距。反常光谱关联的存在如何影响量子信息的置乱？该方案旨在解决这一问题，并在孤立和开放的量子多体系统中分析提取光谱统计和动力学的新特征。此外，尽管量子多体系统的光谱统计很重要，但由于难以分辨光谱中的紧密间隔，因此还没有实验测量。该奖学金的第二个目标是与实验学家合作伙伴合作，首次在实验室中的量子多体模拟器中实验测量光谱统计的关键特征。该项目特别及时，因为它加深和加深了对量子系统中多体相互作用在信息置乱和处理中的作用的理解，响应了最近量子混沌的复兴，以及量子多体系统的量子模拟的快速发展。实现这些目标将在构建广泛适用的分析框架方面产生重大影响;在量子多体模拟器中首次实验测量光谱统计;以及在凝聚态，量子信息和高能物理学社区之间建立新的联系。