Interface, Edge and Bulk of Complex States of Matter

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各种类型的相，这些相与日常生活中熟悉的固体、液体和气体非常不同。发现和理解物质的新阶段是凝聚态物理学的中心目标，这可能会导致新技术；量子计算就是一个例子。除了在理论上直接探测它们的体积外，PI和他的团队还将研究如何通过探测它们的边缘以及将它们分开的界面来揭示这些新相的一些特性。理论结果有助于指导同一主题的实验和数值模拟。它们也可能引起其他物理学领域的研究人员的兴趣，包括高能物理学和引力物理学。这项研究包括对一些量子霍尔相的研究，它发生在半导体界面上的二维电子片中，冷却到非常低的温度，并放置在垂直于片的很强的磁场中。PI将专注于那些理论认为表现出奇异量子力学状态的阶段，这些状态的精确性质需要与实验相协调。此外，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凝聚态教材，反映了过去几十年来该领域的变革性发展。最近，他编写了家庭作业问题的解决手册，已提供给在教学中采用这本书的教师。他将继续这方面的工作，包括创建和维护在线勘误。这样的工作将进一步促进这一领域学生的教育。该奖项支持具有强相互作用的多粒子系统的奇异量子相的理论研究和教育。其中一些相具有拓扑性质。该项目的主要焦点之一是分离不同拓扑相的边缘和界面的物理性质，以及它们与所涉及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，以及由这种界面的量子涨落引发相变的可能性。本项目的另一个重点是将无间隙费米子系统的费米面视为相空间中的边界，这是一个非交换的；PI和他的团队将使用Seiberg-Witten映射将这样的系统映射到它们的交换对应体并揭示它们的性质。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，包括密度矩阵重整化群，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，其中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。此外，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凝聚态教材，反映了过去几十年来该领域的变革性发展。最近，他编写了家庭作业问题的解决手册，已提供给在教学中采用这本书的教师。他将继续这方面的工作，包括创建和维护在线勘误。这样的工作将进一步促进这一领域学生的教育。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 types of phases, which are very different from those familiar from daily life, like solid, liquid and gas. The discovery and understanding of new phases of matter is a central goal of condensed matter physics, which may lead to new technologies; quantum computation might be one example. In addition to directly probing their bulk in theory, the PI and his team will study how to reveal the properties of some of these new phases by probing their edges, as well as the interfaces that separate them. Theoretical results help guide experimental as well as numerical simulations on the same subject. They may also be of interest to researchers in other fields of physics, including high-energy and gravitational physics.Included in this research is the study of some quantum Hall phases, which occur in a two-dimensional sheet of electrons trapped at an interface between semiconductors, cooled to very low temperatures, and placed in an a very strong magnetic field perpendicular to the sheet. The PI will focus on phases that theory suggests exhibit exotic quantum mechanical states the precise nature of which need to be reconciled with experiments. In addition, 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 over the last few decades. More recently he prepared the solution manual for its homework problems, that has been made available to instructors adopting this book in their teaching. He will continue his work in this direction, including creating and maintaining an online erratum. Such work will further facilitate education of students in this field.TECHNICAL SUMMARYThis award supports theoretical research and education on exotic quantum phases of many-particle systems with strong interactions. Some of these phases are of topological nature. One of the main foci of this project is the physical properties of the edges and interfaces separating different topological phases, and their relations to the topological properties of the phases involved. 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 of such interfaces. Another thrust of this project is to view the Fermi surface of gapless fermion systems as a boundary in the phase space, which is a non-commutative; the PI and his team will use the Seiberg-Witten mapping to map such systems to their commutative counterparts and reveal their properties.The PI and his team will use a combination of theoretical and numerical tools in their studies, including density matrix renormalization group, bosonization, and exact diagonalization. They will also attempt to borrow insights and methodology from other fields, including string theory, 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.In addition, 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 over the last few decades. More recently he prepared the solution manual for its homework problems, that has been made available to instructors adopting this book in their teaching. He will continue his work in this direction, including creating and maintaining an online erratum. Such work will further facilitate education of students in this field.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.