Exotic Phases and Their Interfaces in Correlated Many-Particle Systems

该奖项支持对具有强相互作用的多粒子系统的奇异性质的理论研究和教育。众所周知，粒子之间的强相互作用可以稳定物质的各个阶段，这些阶段可能与日常生活中熟悉的物质非常不同，如固体、液体和气体。理解这些相是凝聚态物理学的一个重要目标，它可能为量子计算等技术应用铺平道路。PI和他的团队将研究如何通过探测分离它们的界面来揭示一些新相的特性。理论结果有望帮助指导相关的实验和模拟。这项研究也可能引起其他物理学领域的兴趣，包括高能物理学和引力物理学。该奖项支持的研究活动将把研究生引入凝聚态物理的前沿。最近，PI出版了一本新的研究生水平的凝聚态教材，反映了这个领域在过去几十年里的变革性发展。他将继续这个方向的工作，包括为家庭作业问题制定解决手册。这样的工作将进一步促进这一领域学生的教育。该奖项支持对具有强相互作用的多粒子系统的奇异量子相的理论研究。其中一些相具有拓扑性质。这个项目的一个主要焦点是研究分离不同拓扑相的界面的物理性质，以及它们与单个相的拓扑性质的关系。例子包括阿贝尔和非阿贝尔量子霍尔相之间的界面，以及具有相同填充因子但具有不同拓扑顺序的不同非阿贝尔相之间的界面。PI和他的团队将研究这种界面的静态和动态特性，以及界面上量子波动引发相变的可能性。该项目的另一个重点是利用量子信息理论中的概念，包括纠缠和柯尔莫哥洛夫复杂性，来表征典型和非典型激发态。这里的目标是获得对孤立量子系统中热化的更深入的理解。该项目的第三个重点是使用耦合线方法来理解准一维系统中的超固体性。PI和他的团队将在他们的研究中使用理论和数值工具的结合，包括平均场理论，重整化群，玻色子化和精确对角化。他们还将尝试借鉴其他领域的见解和方法，包括弦理论和黑洞物理学，这些领域的相关问题已经得到了广泛的研究。这将为研究生提供宝贵的培训机会，并促进不同领域之间的协同作用。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports theoretical research and education on exotic properties of many-particle systems with strong interactions. It is known that strong interactions between particles can stabilize various phases of matter that can be very different from those familiar from daily life, like solid, liquid and gas. Understanding such phases is an important goal of condensed matter physics, which may pave the way to technological applications like quantum computation. The PI and his team will study how to reveal the properties of some new phases by probing the interfaces that separate them. Theoretical results are expected to help guide associated experiments and simulations. The research may also be of interest to other fields of physics, including high-energy and gravitational physics.The research activities supported by this award will introduce graduate students to the frontier of condensed matter physics. Recently the PI has published a new graduate level condensed matter textbook, that reflects the transformative developments of this field in the last few decades. He will continue his work in this direction, including working out a solutions manual for its homework problems. Such work will further facilitate education of students in this field.TECHNICAL SUMMARYThis award supports theoretical research on exotic quantum phases of many-particle systems with strong interactions. Some of these phases are of topological nature. A main focus of this project is to investigate physical properties of interfaces separating different topological phases, and their relationship to the topological properties of the individual phases. Examples include interfaces between Abelian and non-Abelian quantum Hall phases, and between different non-Abelian phases at the same filling factor but with different topological order. The PI and his team will study both the static and dynamical properties of such interfaces, and the possibility of phase transitions triggered by quantum fluctuations at the interfaces. Another focus of this project is to characterize typical and atypical excited states using concepts from quantum information theory, including entanglement and Kolmogorov complexity. The goal here is to gain deeper understanding of thermalization in isolated quantum systems. A third focus of the project is to understand supersolidity in quasi-one-dimensional systems, using the coupled-wire approach.The PI and his team will use a combination of theoretical and numerical tools in their studies, including mean-field theory, renormalization group, bosonization, and exact diagonalization. They will also attempt to borrow insights and methodology from other fields, including string theory and black hole physics, in which related issues have been studied extensively. These will provide valuable training opportunities for graduate students, as well as stimulating synergy among different fields.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.