Understand
Immersion (i.e., local embedding) is relevant to the physics of topologically ordered phases through the entanglement bootstrap.
- An annulus can be immersed in a disk or a sphere as a "figure-8", which cannot be smoothly deformed to an embedded annulus.
- We investigate a simple problem: is there an Abelian state on the immersed figure-8 annulus, locally indistinguishable from the ground state of the background physical system? We show that if the answer is affirmative, a strong sense of isomorphism must hold: two homeomorphic immersed regions must have isomorphic information convex sets, even if they cannot smoothly deform to each other on the background physical system.
- We explain why to care about strong isomorphism in physical systems with anyons and give proof in the context of Abelian anyon theory.