CAREER: Equilibrium and Dynamics of Strongly Interacting Many-body Systems

材料研究部和物理部为该职业奖提供资金，以支持理论量子多体物理的综合研究和教育工作。量子多体物理学研究包含大量组分的量子力学系统的行为。由于系统的量子力学性质和大量成分，可以出现通常在经典系统中没有直接类比的奇异物理特性。特别有趣的是，这个项目的重点是强相关的系统，其中系统的组件彼此之间强烈地相互作用，将系统带入一个完全不同的状态，而不是那些在非相互作用或弱相互作用系统中遇到的系统。该项目旨在研究这些系统中新特征的理论基础，这些特征是由于平衡和动态过程中的强相互作用而成为可能的。通过构建新的理论模型和设计实验可行的方法来探索预测的性质，不仅加深了我们对凝聚态物理中强相关现象的理解，而且有助于它们在量子信息论、量子场论和冷原子实验中的研究和应用。此外，作为项目教育部分的一部分，该项目旨在通过为高年级本科生和研究生开设“多体纠缠和拓扑阶段”的新课程，以及为当地高中生组织“量子国际象棋”锦标赛，将量子力学和量子多体物理的新概念整合到推广和教育活动中，其中很大一部分学生来自代表性不足的群体。比赛的目标是通过有趣的游戏向高中生介绍量子力学的基本概念。技术概述材料研究部和物理部为该职业奖提供资金，以支持理论量子多体物理的综合研究和教育工作。该项目的目标是促进对量子多体系统的基本理解，包括平衡和动态过程。研究重点是强相互作用系统，探索非相互作用系统中不存在的新颖拓扑现象和多体动力学。PI将依靠她之前对精确可解晶格模型的研究，以及对场论分析和张量网络数值方法的研究来解决这些问题。特别是，本项目将重点关注以下主题：i)构建和分析新的三维离散规范理论；ii)利用耦合层结构解释和推广三维分形量子码的拓扑顺序，并伴随潜在的量子信息应用；iii)用实验可行的测量方案在扩散和多体局域系统中映射Lieb-Robinson光锥。PI将探索强相互作用量子多体系统的非摄动状态，并将寻找根本的新普遍行为。潜在的成就包括：i)发现新的三维扭曲规范理论，并了解它们在体和表面的性质；Ii)寻找将分形量子码与更常规的拓扑顺序连接起来的广义拓扑相图，构建更多可作为量子记忆的物理模型；(3)了解各种相关测量在检测扩散或多体局部系统中信息传播的能力，并找到实验上可行的实现这种测量的装置。此外，作为项目教育部分的一部分，该项目旨在通过为高年级本科生和研究生开设“多体纠缠和拓扑阶段”的新课程，以及为当地高中生组织“量子国际象棋”锦标赛，将量子力学和量子多体物理的新概念整合到推广和教育活动中，其中很大一部分学生来自代表性不足的群体。比赛的目标是通过有趣的游戏向高中生介绍量子力学的基本概念。

NONTECHNICAL SUMMARYThe Division of Materials Research and the Division of Physics contribute funds to this CAREER award, which supports an integrated research and educational effort on theoretical quantum many-body physics. Quantum many-body physics studies the behavior of quantum mechanical systems that contain a large number of constituents. Due to both the quantum mechanical nature of the systems and the large number of constituents, exotic physical properties can emerge that usually do not have a direct analog in classical systems. Of particular interest, and the focus of this project, are strongly correlated systems where the components of the system interact strongly with each other, taking the system into a completely different regime than those encountered in non-interacting or weakly interacting systems. This project aims to study the theoretical foundations of new features in these systems that are made possible due to the strong interactions, both at equilibrium and in dynamical processes. By constructing new theoretical models and by designing experimentally feasible ways to probe the predicted properties, the project aims to not only deepen our understanding of strongly correlated phenomena in condensed matter physics, but to also contribute to their study and application in quantum information theory, quantum field theory, and cold-atom experiments.Moreover, as part of the educational component of the project, the PI aims to integrate novel concepts of quantum mechanics and quantum many-body physics into outreach and educational activities by developing a new course on "Many-body Entanglement and Topological Phases" for senior undergraduate and graduate students, and by organizing a "quantum chess" tournament for local high-school students, a large proportion of which are from underrepresented groups. The goal of the tournament is to introduce the basic concepts of quantum mechanics to high-school students through engaging games.TECHNICAL SUMMARYThe Division of Materials Research and the Division of Physics contribute funds to this CAREER award, which supports an integrated research and educational effort on theoretical quantum many-body physics. The goal of the project is to advance the fundamental understanding of quantum many-body systems, both at equilibrium and in dynamical processes. The research focuses on systems with strong interactions, and explores novel topological phenomena and many-body dynamics, which cannot exist in non-interacting systems. The PI will rely on her previous research on exactly solvable lattice models, and on field-theory analysis and tensor-network numerical approaches to tackle these problems. In particular, this project will focus on the following topics:i) Constructing and analyzing new discrete gauge theories in 3D,ii) Interpreting and generalizing the topological order in 3D fractal quantum codes using a coupled-layer construction, with concomitant potential quantum-information applications,iii) Mapping the Lieb-Robinson light cone in diffusive and many-body localized systems with experimentally feasible measurement schemes.The PI will explore the non-perturbative regime of strongly interacting quantum many-body systems, and will look for fundamentally new universal behavior. Potential achievements include: i) discovering new twisted-gauge theories in 3D and understanding of their properties both in the bulk and on the surface; ii) finding a generalized topological phase diagram which connects the fractal quantum code to more conventional topological orders, and constructing more physical models that can serve as quantum memories; (3) understanding the ability of various correlator measures in detecting information propagation in diffusive or many-body localized systems, and finding experimentally feasible setups for realizing such measurements.Moreover, as part of the educational component of the project, the PI aims to integrate novel concepts of quantum mechanics and quantum many-body physics into outreach and educational activities by developing a new course on "Many-body Entanglement and Topological Phases" for senior undergraduate and graduate students, and by organizing a "quantum chess" tournament for local high-school students, a large proportion of which are from underrepresented groups. The goal of the tournament is to introduce the basic concepts of quantum mechanics to high-school students through engaging games.