The uses of lattice topological defects
CMSA EVENTS: CMSA QUANTUM MATTER IN MATH & PHYSICS SEMINAR
I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse topological defects in two-dimensional classical lattice models and quantum chains.
These defects possess a variety of remarkable properties. Not only is the partition function independent of deformations of their path, but they can branch and fuse in a topologically invariant fashion. One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum. The universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice. I also will describe how terminating defect lines allows the construction of fractional-spin conserved currents, giving a linear method for Baxterization, I.e. constructing integrable models from a braided tensor category.