Classification of topologically ordered phases of matter in 2D
In this talk I will consider topological phases of matter which have what is
called long range entanglement (LRE). Ground states with LRE in a non-trivial
phase cannot be converted into a product state using only (sufficiently) local
operations. An interesting aspect is that such states can support quaisparticles
with braided statistics, called anyons. I will compare different approaches to
extracting the algebraic properties of these anyons from first principles, and
explain how this relates to the classification of topologically ordered phases.
I will then highlight some recent developments and current challenges in the field.