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

非技术总结该奖项支持有关基本方面的理论研究和教育，如教科书中对物质的描述，如流体动力学和热力学，如何以及是否来自由许多微小相互作用的粒子组成的系统，如原子或电子。最近在多体局部化现象方面的进展突显了传统热力学描述崩溃的可能性。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，并调查有趣的中间状态在教科书热力学和完全多体定域相之间连续插入的可能性。在不相互作用的粒子的波形图中，随机缺陷的散射会导致波之间的破坏性干涉，从而产生局域化的不导电的量子力学状态。人们认为，开启粒子之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建模局域态的量子控制，探测多体局域化的新实验方案，以及特别有利于这些现象的数值研究的奇异模型的设计，以及系统地在经典和量子力学物质模拟之间进行外推的新近似方案。这些理论研究还将补充和指导正在进行的使用超冷原子气体等系统“模拟”多体定位的实验工作。该项目将有助于培养凝聚态物理和更广泛的多体动力学领域的本科生和研究生。PI将继续在本科生、研究生和博士后研究人员中指导不同的学生。国际和平研究所将继续在研究生院组织会议和每周研讨会，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社区做出贡献，包括通过组织工作坊。技术总结该奖项支持理论研究和教育，以研究激发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，它被广泛定义为强激发多体动力学的停滞遍历，在有限温度下有效，或者更好地说，有限粒子的有限熵。在某些量子模型中，一种尖锐的动力学跃迁有望将局域相与扩散相分离。经典多体动力学的自旋模型中存在这样的跃迁，这是一个有趣的可能性，之前PI和合作者曾用数值方法探索过，但由于局域经典混沌的普遍存在，暂时排除了这种可能性。研究议程有两个互补的部分。第一部分将集中于开发用于研究多体定位模型的概念和数值工具，以克服常用方法的局限性。最近由Pi等人为完全多体局域光谱引入的出现可积性现象学将被简化，但也将扩展到可能存在附近迁移率边缘的情况。使用矩阵积态的高效变分方法将被开发来计算超长自旋链的激发本征态，也可以用来近似“经典”轨道附近的多体动力学。同时，研究议程的第二部分将在新的环境下探索多体局域化的概念：陷阱中的多体局域化，多体局域化的自对偶模型，多体局域化内的希尔伯特玻璃相的绝热退火。这三个特定于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普遍的见解。这个项目将有助于培养凝聚态物理和更广泛的多体动力学领域的本科生和研究生。PI将继续在本科生、研究生和博士后研究人员中指导不同的学生。国际和平研究所将继续在研究生院组织会议和每周研讨会，为城市大学、纽约和附近机构的研究界提供服务。国际凝聚物社还将继续寻找机会，包括通过组织讲习班等方式，为国际凝聚物界作出贡献。

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.