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

该奖项支持理论研究和教育的基本方面，如何以及是否物质的描述，如流体动力学和热力学呈现在教科书中出现从许多微小的相互作用的粒子，如原子或电子组成的系统。一种被称为多体定位的现象的最新进展突出了打破传统热力学描述的可能性。PI将对模型系统进行理论研究，以探索和量化这种分解的程度，并调查在教科书热力学和完全多体局域相之间不断插入有趣的物质中间状态的可能性。在不相互作用的粒子的波图中，来自随机缺陷的散射会导致波之间的破坏性干涉，从而产生局域化且不导电的量子力学状态。据认为，打开粒子之间的相互作用可以导致一种动态形式的定位，即多体定位，这是本研究项目的一个概念成分。这项工作的一个重要分支是对局域态的量子控制的探索和建模，用于检测多体局域的新实验方案，以及特别有利于这些现象的数值研究的奇异模型的设计，以及在物质的经典和量子力学模拟之间进行系统外推的新近似方案。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”使用超冷原子气体等系统的多体定位。本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。PI将继续在研究生中心组织会议和每周一次的研讨会，为纽约城市大学和附近机构的研究界提供服务。PI还将继续寻求机会，通过组织研讨会等方式为国际凝聚态物质社区做出贡献。该奖项支持理论研究和教育，以研究激发态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部化现象，它被广泛地定义为强激发多体动力学的停滞遍遍性，有效地在有限温度下，或者更好地，在每个粒子的有限熵下。在某些量子模型中，预期会有一个尖锐的动力学跃迁将局域相与扩散相分离。在经典多体动力学的自旋模型中存在这样的跃迁是一个有趣的可能性，以前由PI和合作者在数值上探索过，但由于局部经典混沌的普遍存在而暂时排除了这种可能性。研究议程有两个互补的部分。第一部分将侧重于开发概念和数值工具来研究多体定位模型，以克服常用方法的局限性。PI等人最近为完全多体局域谱引入的涌现可积现象学将被简化，但也将扩展到可能存在附近迁移边缘的情况。利用矩阵积态的有效变分方法将被开发来计算超长自旋链的激发态，也可以近似“经典”轨迹附近的多体动力学。与此同时，研究议程的第二部分将探索新环境下的多体定位概念：陷阱中的多体定位，多体定位的自对偶模型，多体定位内的希尔伯特玻璃相绝热退火。这三个特定模型的研究中的每一个都有望对这些动态转变的物理学产生一般的见解。本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。PI将继续在研究生中心组织会议和每周一次的研讨会，为纽约城市大学和附近机构的研究界提供服务。PI还将继续寻求机会，通过组织研讨会等方式为国际凝聚态物质社区做出贡献。

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.