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.

非技术摘要这一奖项支持理论研究和教育，内容涉及有关物质的基本方面，例如，从教科书中介绍的物质的描述（例如流体动力学和热力学）是由许多由许多小型相互作用粒子（例如原子或电子）组成的系统中出现的。 在一种称为多体定位的现象上的最新进展突出了传统热力学描述崩溃的可能性。 PI将对模型系统进行一项理论研究，以探索和量化这种分解的程度，并研究有趣的物质中间状态在教科书热力学和完全多体局部相之间连续插值的中间状态。 在不相互作用的颗粒的波浪中，从随机缺陷的散射导致波浪之间的破坏性干扰，导致量子机械状态局部且不会导致电力。人们认为，粒子之间的交互作用可以导致一种动态的定位形式，多体定位，这是该研究项目中的概念成分。这项工作的重要分支是对局部状态的量子控制的探索和建模，新颖用于检测多体定位的实验方案，以及外来模型的设计，特别有利于对这些现象的数值研究和新型近似方案的数值研究，以系统地推断物质的经典和量子机械模拟之间。这些理论研究还将补充和指导正在进行的实验努力，以使用Ultracold Atomic Gases等系统“模仿”多体定位。该项目将有助于培训凝聚态物理学和多体动力学领域的培训本科生和研究生。 PI将继续指导本科，研究生级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社区服务。 PI还将继续寻求机会为国际冷凝的物质社区做出贡献，包括通过研讨会的组织。科学摘要这一奖项支持理论研究和教育，以调查兴奋但孤立的多体系统的动态现象。这里的主要物理动机是多体定位的现象，该现象被广泛地定义为强烈激发多体动力学的导致的超高性，在有限的温度下有效或每个粒子的有限熵。在某些量子模型中，预计急剧的动态跃迁将与扩散相分开。经典多体动力学的自旋模型中的这种过渡的存在是PI和合作者在数值上探索的一种有趣的可能性，并且由于局部经典混乱的率而暂时排除了。 研究议程有两个互补的部分。第一部分将集中于开发概念和数值工具，用于研究克服常用方法局限性多体定位模型。 PI和其他针对完全多体的局部光谱最近引入的新出现可集成性的现象学将被简化，但也扩展到可能存在附近的流动性边缘的情况。使用矩阵 - 产品态将开发出有效的变分方法，以计算非常长的自旋链的激发特征状态，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讨新型环境中多体定位的概念：陷阱中的多体定位，多体定位的自偶像模型，绝热退火到希尔伯特玻璃相中身体定位。这三个模型的特定研究中的每一个都有望对这些动力学转变的物理学产生一般见解。该项目将有助于培训凝结物理学和多体动态领域的本科生和研究生。 PI将继续指导本科，研究生级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社区服务。 PI还将继续寻求机会为国际冷凝的物质社区做出贡献，包括通过组织研讨会。