Emergence & Entanglement II 2013
In two spatial dimensions, there is a good correspondence between TQFTs and topological phases of matter for spin systems. I will discuss this correspondence in one and three spatial dimensions for spin systems. If time permits, I will also discuss the situation for fermion systems.
I will discuss recent work on 3d Symmetry Protected Topological (SPT) phases of bosonic systems, and their implications for understanding the more exotic quantum spin liquid phases. First I will describe various characterizations of these 3d SPT phases, in particular their surface effective theories and (when applicable) bulk electromagnetic response. Next I will show how this understanding leads to several new insights into the theory of both 2d and 3d quantum spin liquids. Finally I will provide an explicit construction of several 3d SPT phases in a system of `coupled layers'.