Speaker
Daniel Wallick, Ohio State University
Abstract
Naaijkens’ superselection theory provides an operator-algebraic description of anyonic excitations for (2+1)-dimensional topologically ordered quantum spin systems. This approach has proven to be a useful method to describe the physics of these systems mathematically rigorously in the infinite volume. Notably, these anyonic excitations form a braided tensor category. Our work generalizes Naaijkens’ methods to include symmetry-enriched topological orders. These are topologically ordered spin systems that also have a symmetry action by a finite group G. Given an onsite G-action for a quantum spin system and a G-invariant state \omega_0, we define a notion of G-defect sector that extends Naaijkens’ definition of anyon superselection sector. Under suitable assumptions, we show that the G-defect sectors form a G-crossed braided tensor category, as expected from the physics literature. We compute this category for some short-range and long-range entangled models. This is joint work with Kyle Kawagoe and Siddharth Vadnerkar.