Non-perturbative and stochastic approaches to many-body localization

多体定位的非扰动随机方法

• 批准号: EP/P010180/1
• 负责人: Henning Schomerus
• 金额: $ 47.72万
• 依托单位: Lancaster University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FP010180%2F1
• 关键词: Non; perturbative; stochastic; approaches; many

A central question in physics concerns the complexity of any given system. What is the nature of quantities characterising the system behaviour, and which characteristics can be safely ignored? How sensitive is the system against external perturbations and how predictable is its dynamics? How many parameters need to be controlled to manipulate the system in a specific way? These questions not only lie at the heart of fundamental fields such as statistical mechanics, but also provide the key to the characterisation of equilibrium phases and nonequilibrium dynamics and pervade practical applications in quantum information, control and sensing.Meeting the urgent need to understand these questions in the quantum setting, the scientific community has recently identified a key paradigm that should hold many of the required answers. This concerns large but finite many-body systems with disorder, low spatial dimensionality and local interactions. These ingredients have been seen to conspire in a persistence of local memory of initial conditions, a fascinating phenomenon known as many-body localisation (MBL). The understanding of this phenomenon is still in its infancy. The theoretical arguments for MBL are thorough, but also in essence qualitative, while quantitative insight to date mainly arrives from numerical investigations of relatively small (in real-world terms) systems. This state of affairs has given rise to a proliferation of characterisations based, among others, on transport, thermalisation, entanglement, dynamics, whose detailed mutual relationships are mostly unclear. These shortcomings become even more pressing as the very first dedicated experiments target yet another set of characteristics, the directly observable consequences in real-world systems.In this project, we take a step back and ask the question: which level of understanding could be accepted to constitute a rather complete description of many-body localisation and delocalisation? Taking a leaf out of the book from non-interacting systems, we argue that this has to involve, as a central piece, a statistical description in quasi-one dimensional settings. We approach this goal from (I.) a rich one-dimensional model system originating from lattice field theory (the Schwinger model, a version of quantum electrodynamics) which is amenable to a detailed treatment and (II.) a stochastic description based on fundamental composition rules of the density matrix (the key object to describe entanglement), allowing comprehensive access to the generic system behaviour. Amongst the observable consequences, we aim to (III.) discriminate between general and system-specific aspects in the MBL phase and of the phase transition, including experimentally testable signatures, and (IV.) extend the considerations to topological phases, where the system displays order due to intricate quantum effects.

物理学中的一个核心问题涉及到任何给定系统的复杂性。表征系统行为的量的性质是什么？哪些特性可以安全地忽略？系统对外部扰动的敏感度有多高，其动态的可预测性有多高？需要控制多少参数才能以特定方式操纵系统？这些问题不仅位于统计力学等基础领域的核心，而且为描述平衡相和非平衡动力学提供了关键，并渗透到量子信息、控制和传感的实际应用中。为了满足在量子环境下理解这些问题的迫切需要，科学界最近确定了一个关键范式，它应该包含许多所需的答案。这涉及到具有无序、低空间维度和局部相互作用的大型但有限的多体系统。这些因素被认为共同作用于对初始条件的局部记忆的持久存在，这是一种被称为多体定位(MBL)的迷人现象。对这一现象的理解还处于初级阶段。关于MBL的理论论证是彻底的，但在本质上也是定性的，而迄今为止的定量见解主要来自对相对较小的(在现实世界中)系统的数字调查。这种情况导致了基于运输、热化、纠缠、动力学等特征的激增，这些特征的详细相互关系大多不清楚。这些缺点变得更加紧迫，因为第一个专门的实验针对的是另一组特征，即真实世界系统中直接可见的后果。在这个项目中，我们退一步问一个问题：什么样的理解水平可以被接受，以构成对多体局部化和非局部化的相当完整的描述？借鉴非相互作用系统的经验，我们认为，作为核心，这必须涉及准一维环境中的统计描述。我们从(I)开始实现这一目标。源于格子场理论的丰富的一维模型系统(Schwinger模型，量子电动力学的一个版本)，它可以经过详细的处理和(Ii)。基于密度矩阵(描述纠缠的关键对象)的基本组成规则的随机描述，允许全面访问一般系统行为。在可观察到的后果中，我们的目标是(Iii)区分MBL阶段和相变阶段的一般和系统特定方面，包括可通过实验测试的特征，以及(Iv)。将考虑扩展到拓扑阶段，在拓扑阶段，由于复杂的量子效应，系统显示出秩序。

项目成果

Insights into Low-Dimensional Many-Body Localised Systems

深入了解低维多体局部系统

• DOI: 10.17635/lancaster/thesis/1664
• 发表时间: 2022
• 作者: Chen C

Universal hypotrochoidic law for random matrices with cyclic correlations

具有循环相关性的随机矩阵的通用次摆轮线定律

• DOI: 10.48550/arxiv.1812.07055
• 发表时间: 2018
• 作者: Aceituno P

One-particle density matrix characterization of many-body localization

• DOI: 10.1002/andp.201600356
• 发表时间: 2017-07-01
• 期刊: ANNALEN DER PHYSIK
• 影响因子: 2.4
• 作者: Bera, Soumya;Martynec, Thomas;Bardarson, Jens H.
• 通讯作者: Bardarson, Jens H.

Supersymmetric Polarization Anomaly in Photonic Discrete-Time Quantum Walks.

• DOI: 10.1103/physrevlett.121.260501
• 发表时间: 2018-04
• 期刊: Physical review letters
• 影响因子: 8.6
• 作者: S. Barkhofen;L. Lorz;Thomas Nitsche;C. Silberhorn;H. Schomerus

Diagnostics of entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition

通过测量引起的稳态纠缠跃迁诊断噪声和无序自旋链中的纠缠动力学

• DOI: 10.1103/physrevb.105.144202
• 发表时间: 2022
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Boorman T