On the classification of (2+1)D topological order via modular fusion categoriesMathematical Physics Seminar
|Speaker:||Colleen Delaney, UC Berkeley|
|Start time:||Mon, Oct 23 2023, 3:10PM|
Typically two 2d quantum systems exhibiting distinct topological order can be distinguished from each other simply by comparing the behavior of the ground states on a torus under modular transformations (S and T matrices). However, there are examples which can not be distinguished in this manner and in practice require one to understand the more fine-grained characterization of topological order via modular fusion categories. Such ``modular isotopes" can even occur in generally well-understood theories, namely twisted quantum double models. I will give an accessible review of modular fusion category theory from both the points of view of a physicist and a mathematician, and then argue that both are helpful for fully appreciating the distinction between these examples of topological order.