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，该奖项支持理论量子多体物理学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的成分，奇异的物理性质可以出现，通常在经典系统中没有直接的模拟。特别感兴趣的是，这个项目的重点是强相关系统，其中系统的组件相互作用强烈，使系统进入一个完全不同的制度，而不是在非相互作用或弱相互作用系统中遇到的。该项目旨在研究这些系统中由于平衡和动态过程中的强相互作用而可能产生的新特征的理论基础。通过构建新的理论模型和设计实验可行的方法来探测预测的性质，该项目的目的不仅是加深我们对凝聚态物理中强关联现象的理解，而且还有助于它们在量子信息理论、量子场论和冷原子实验中的研究和应用。此外，作为该项目教育部分的一部分，该计划旨在将量子力学和量子多体物理学的新概念融入外展和教育活动中，为高年级本科生和研究生开设了一门新的“多体纠缠和拓扑相位”课程，并为本地高中生组织了一场“量子国际象棋”比赛，其中大部分学生来自代表性不足的群体。比赛的目的是通过引人入胜的游戏向高中生介绍量子力学的基本概念。技术概要材料研究部和物理部为该职业奖提供资金，支持理论量子多体物理学的综合研究和教育工作。该项目的目标是推进量子多体系统的基本理解，无论是在平衡和动力学过程。 研究重点是强相互作用的系统，并探索新的拓扑现象和多体动力学，这在非相互作用系统中不存在。PI将依靠她以前对精确可解晶格模型的研究，以及场论分析和张量网络数值方法来解决这些问题。特别是，这个项目将集中在以下主题：i）在3D中构建和分析新的离散规范理论，ii）使用耦合层结构解释和推广3D分形量子码中的拓扑顺序，以及随之而来的潜在量子信息应用，iii）用实验可行的测量方案映射扩散和多体定域系统中的Lieb-Robinson光锥。PI将探索强相互作用量子多体系统的非微扰机制，并将寻找全新的普适行为。可能取得的成就包括：i）发现新的3D扭曲规范理论，并理解它们在体和表面上的性质; ii）找到将分形量子码与更传统的拓扑序联系起来的广义拓扑相图，并构建更多可以作为量子存储器的物理模型;（3）理解各种相关器测量在检测扩散或多体局域系统中的信息传播的能力，并找到实验上可行的装置来实现这种测量。此外，作为该项目教育部分的一部分，PI的目标是通过开发一门新的课程，将量子力学和量子多体物理学的新概念融入到推广和教育活动中，为高年级本科生和研究生举办“多体纠缠和拓扑相位”，并为当地高中生组织“量子国际象棋”锦标赛，其中很大一部分学生来自代表性不足的群体。比赛的目标是通过引人入胜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.