New topological structures in condensed matter physics

这项研究位于数学(低维和量子拓扑)和理论凝聚态物理(可积晶格模型)的交界处，与拓扑量子计算有关。用拓扑量子场论(TQFT)描述的凝聚态物理中拓扑相的存在是一个具有重要意义的发现。本研究项目的主要目的之一是研究(21)维拓扑量子场论与可积晶格模型之间的一般关系。数学方面引入了来自低维拓扑学、表示理论、组合学的各种工具。PI计划从物理角度获得更深层次的洞察，在圣巴巴拉的卡夫利理论物理研究所(KITP)花费部分时间获得拨款支持，并与他的家乡弗吉尼亚大学的物理学教师合作。作为这一项目的结果，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的合作。

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.