New topological structures in condensed matter physics

University Of Virginia Main Campus, Charlottesville VA

Investigators

Abstract

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.