Speaker: Dominic Williamson (University of Vienna)

Title: State sum topological quantum field theories and tensor networks: from Z to A

Abstract: I will describe the connection between state sum constructions of topological quantum field theories and commuting projector Hamiltonians that are simple representatives for certain topological phases of matter in systems of strongly interacting quantum spin degrees of freedom on a lattice. Such Hamiltonians are called Levin-Wen string-net models by the theoretical condensed matter community, although this usually refers to 2+1 dimensions. Along the way I will point out the interpretation of state sums as tensor networks. This point of view yields tensor network constructions for ground states of the aforementioned Hamiltonians. A particularly interesting consequence of topological invariance for a state sum is the existence of certain operators that commute with the individual tensors used to build the relevant ground state. I will discuss the implications of these 'symmetry' operators for the presence of topological order in the models.