Quantum and semi-classical dynamics of random spin chains: models and methods for quantum non-ergodic statistical physics

随机自旋链的量子和半经典动力学：量子非遍历统计物理的模型和方法

• 批准号: 1508538
• 负责人: Vadim Oganesyan
• 金额: $ 30万
• 依托单位: CUNY College of Staten Island
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-01-15 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1508538&HistoricalAwards=false
• 关键词: Quantum; semi; classical; dynamics; random

NONTECHNICAL SUMMARYThis award supports theoretical research and education on fundamental aspects of how and whether descriptions of matter, such as fluid dynamics and thermodynamics presented in textbooks emerge from a system composed of many tiny interacting particles, such as atoms or electrons. Recent progress on a phenomenon known as many-body localization highlights the possibility of a breakdown of the conventional thermodynamic description. The PI will carry out a theoretical study of model systems to explore and quantify the degree of this breakdown and to investigate the possibility that interesting intermediate states of matter interpolate continuously between textbook thermodynamics and fully many-body localized phases. In a wave picture of particles that do not interact, scattering from random imperfections leads to destructive interference among the waves resulting in quantum mechanical states that are localized and do not conduct electricity. It is thought that turning on interactions among particles can lead to a dynamical form of localization, many-body localization, a conceptual ingredient in this research project.A significant offshoot of this work is the exploration and modelling of quantum control of localized states, novel experimental schemes for detecting many-body localization, and design of exotic models particularly favorable to numerical studies of these phenomena and novel approximation schemes to systematically extrapolate between classical and quantum mechanical simulations of matter. These theoretical studies will also complement and guide ongoing experimental efforts to "imitate" many-body localization using systems like ultracold atomic gases.This project will contribute to training undergraduate and graduate students in the field of condensed matter physics and many-body dynamics more generally. The PI will continue mentoring diverse students at the undergraduate, graduate levels and postdoctoral researchers. The PI will continue to organize conferences and a weekly seminar at the Graduate Center, serving the research community at the City University, New York and nearby institutions. The PI will also continue to seek opportunities to contribute to international condensed matter community including through organization of workshops.TECHNICAL SUMMARYThis award supports theoretical research and education to investigate dynamical phenomena in excited but isolated many-body systems. The primary physical motivation here is the phenomenon of many-body localization which is broadly defined as stalled ergodicity of strongly excited many-body dynamics, effectively at finite temperature or, better, finite entropy per particle. In certain quantum models a sharp dynamical transition is expected to separate localized from diffusive phases. Existence of such a transition in spin models of classical many-body dynamics is an intriguing possibility previously explored numerically by the PI and collaborators and tentatively ruled out due to prevalence of localized classical chaos. There are two complementary parts to the research agenda. The first part will be focused on developing conceptual and numerical tools for studying models of many-body localization that overcome limitations of commonly used methods. The phenomenology of emergent integrability recently introduced by PI and others for fully many-body localized spectra will be streamlined but also extended to cases where a nearby mobility edge might exist. Efficient variational methods, using matrix-product states will be developed to compute excited eigenstates of very long spin chains, but also to approximate many-body dynamics near "classical" trajectories. In parallel, the second part of the research agenda will explore the notion of many-body localization in novel settings: many-body localization in traps, self-dual models of many-body localization, adiabatic annealing into the Hilbert glass phase inside many-body localization. Each of these three model specific studies is expected to produce general insights into the physics of these dynamical transitions. This project will contribute to training undergraduate and graduate students in the field of condensed matter physics and many-body dynamics more generally. The PI will continue mentoring diverse students at the undergraduate, graduate levels and postdoctoral researchers. The PI will continue to organize conferences and a weekly seminar at the Graduate Center, serving the research community at the City University, New York and nearby institutions. The PI will also continue to seek opportunities to contribute to international condensed matter community including through organization of workshops.

非技术性总结该奖项支持理论研究和教育的基本方面，如何以及是否描述的物质，如流体动力学和热力学在教科书中出现从一个系统组成的许多微小的相互作用的粒子，如原子或电子。 最近的进展被称为多体局域化的现象突出了传统的热力学描述的故障的可能性。 PI将对模型系统进行理论研究，以探索和量化这种崩溃的程度，并研究物质的有趣中间状态在教科书热力学和完全多体局域化阶段之间连续插入的可能性。 在不相互作用的粒子的波图像中，随机缺陷的散射导致波之间的相消干涉，导致量子力学状态被局域化并且不导电。人们认为，开启粒子间的相互作用可以导致一种动力学形式的局域化，即多体局域化，这是本研究项目的一个概念组成部分。这项工作的一个重要分支是探索和模拟局域态的量子控制，探测多体局域化的新实验方案，设计特别有利于这些现象的数值研究的奇异模型和新颖的近似方案，以系统地在物质的经典和量子力学模拟之间进行外推。这些理论研究还将补充和指导正在进行的实验工作，以“模仿”多体局域化使用系统，如超冷原子气体。该项目将有助于培养本科生和研究生在凝聚态物理学和多体动力学领域更普遍。 PI将继续指导本科生，研究生和博士后研究人员的不同学生。PI将继续在研究生中心组织会议和每周一次的研讨会，为城市大学、纽约和附近机构的研究界提供服务。PI还将继续寻找机会，为国际凝聚态物质社区做出贡献，包括组织研讨会。技术总结该奖项支持理论研究和教育，以调查兴奋但孤立的多体系统中的动力学现象。这里的主要物理动机是多体局域化现象，它被广泛定义为强激发多体动力学的停滞遍历性，有效地在有限温度下，或者更好地，每个粒子的有限熵。在某些量子模型中，一个急剧的动力学跃迁被期望将局域相和扩散相分开。在经典多体动力学的自旋模型中存在这样的转变是PI和合作者以前在数值上探索的一种有趣的可能性，由于局部经典混沌的流行，暂时排除了这种可能性。 研究议程有两个相辅相成的部分。第一部分将侧重于开发概念和数值工具，用于研究克服常用方法局限性的多体定位模型。PI和其他人最近为完全多体局域化光谱引入的涌现可积性现象将被简化，但也扩展到附近可能存在迁移率边缘的情况。有效的变分方法，使用矩阵乘积状态将被开发来计算很长的自旋链的激发本征态，但也近似于“经典”轨迹附近的多体动力学。 同时，研究议程的第二部分将探索新环境中的多体局域化概念：陷阱中的多体局域化，多体局域化的自对偶模型，绝热退火到希尔伯特玻璃相内的多体局域化。这三个模型的具体研究预计将产生这些动态转变的物理一般的见解。该项目将有助于培养凝聚态物理和多体动力学领域的本科生和研究生。 PI将继续指导本科生，研究生和博士后研究人员的不同学生。PI将继续在研究生中心组织会议和每周一次的研讨会，为城市大学、纽约和附近机构的研究界提供服务。PI还将继续寻找机会，包括通过组织研讨会，为国际凝聚态物质界做出贡献。