New topological structures in condensed matter physics

该研究处于数学（低维和量子拓扑）和理论凝聚态物理（可积晶格模型）的接口，与拓扑量子计算相关。拓扑量子场论（TQFTs）描述的凝聚态物理中拓扑相的存在是一个非常重要的发现。本研究计划的主要目标之一是研究（2 + 1）维拓扑量子场论与可积格点模型之间的一般关系。数学方面引入了低维拓扑学、表示论、组合学等多种工具。PI计划从物理学的角度获得更深入的见解，将部分时间花在圣巴巴拉的Kavli理论物理研究所（KITP），并与他的家乡弗吉尼亚大学的物理系合作。作为该项目的结果，PI计划与弗吉尼亚大学物理系以及圣巴巴拉的拓扑量子计算小组开展重要合作。

The proposed research lies at the interface of Mathematics (low-dimensional and quantum topology) and theoretical Condensed Matter Physics (integrable lattice models), with relevance to topological quantum computation.The existence of topological phases in condensed matter physics, described by topological quantum field theories (TQFTs), has been a discovery of fundamental importance. One of the main goals of this research project is to study the general relationship between (2+1)-dimensional topological quantum field theories and integrable lattice models. The mathematical side brings in a variety of tools from low-dimensional topology, representation theory, combinatorics.The PI plans to gain a deeper insight from the physics perspective, spending part of the time supported by the grant at the Kavli Institute for Theoretical Physics (KITP) in Santa Barbara, and also collaborating with physics faculty at his home institution, the University of Virginia. As a result of this project, the PI plans to develop significant collaborations with the Physics Department at the University of Virginia and with the group working on topological quantum computation in Santa Barbara.