Knots and entanglement

Abstract

We extend the entanglement bootstrap approach to (3+1)-dimensions. We study knotted excitations of (3+1)-dimensional liquid topological orders and exotic fusion processes of loops. As in previous work in (2+1)-dimensions [1, 2], we define a variety of superselection sectors and fusion spaces from two axioms on the ground state entanglement entropy. In particular, we identify fusion spaces associated with knots. We generalize the information convex set to a new class of regions called immersed regions, promoting various theorems to this new context. Examples from solvable models are provided; for instance, a concrete calculation of knot multiplicity shows that the knot complement of a trefoil knot can store quantum information. We define spiral maps that allow us to understand consistency relations for torus knots as well as spiral fusions of fluxes.

Conformal Field Theory Ground States as Critical Points of an Entropy Function

“…Another nice feature is that because the two conditions only involve the entropies of local regions, the conditions can be checked easily. This program is called entanglement bootstrap and can be applied to other settings, including gapped domain walls [9] and higher dimensions [10].…”