2D topological orders with gapped boundaries - a quantum informational study

Excitations of topological orders could leave footprints on subsystems away from them. We develop a quantum informational tool: information convex (a suitably selected convex set of reduced density matrices on a chosen subsystem) to capture such footprints. To illustrate the usefulness and topological invariant structures of information convex, we study 2D quantum double models, and discuss some rich properties of gapped boundaries in non-Abelian models. Finally, we discuss how the structures of information convex may be observed by ultracold atom experiments.