Operator Algebraic Methods in Topological Phases and Quantum Information

A major discovery in contemporary condensed matter physics was the existence of phases of matter that do not fit in Landau's theory, but instead are "topologically ordered". There, certain properties depend on topological properties of the underlying system. This makes them attractive candidates to build a quantum computer or memory, in particular using quasi-particles called anyons. There are many interesting mathematical connections as well: besides topology, operator algebras, representation theory and modular tensor categories play an essential role.

Supported by this studentship, you will study the mathematical physics of 2D gapped topological phases, with applications to quantum information theory, to find an encompassing theory that covers all known examples. A roadblock is that there is no good way to extract the properties of the anyons from the underlying system. You will use operator algebraic techniques to develop tools to do this directly in the thermodynamic limit