Every (2+1) dimensional lattice model with an energy gap is believed to be described by a topological quantum field theory (TQFT) in the low energy, long wavelength limit. What this means concretely is that every lattice model of this kind is associated with a collection of universal topological data that defines the corresponding TQFT. Physically, this data describes the statistical phases associated with braiding or fusing particle-like excitations of the model. Some of these statistical phases, however, are missing a precise definition that would allow for their computation from a microscopic Hamiltonian. In this talk, I will address this issue by giving a microscopic definition of the F-symbol --- one of the most poorly understood pieces of data that characterize TQFTs. I will also discuss applications of this definition to the computation of anomalies in (1+1) dimensional field theories and lattice models.
HET Seminar at IAS | Michael Levin, University of Chicago | "Bridging the gap between lattice models and TQFT"
Fri, Feb 22, 2019, 1:45 pm
Bloomberg Lecture Hall