TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.14.6.141
TI  - Knots and entanglement
PY  - 2023/06/02
UR  - https://scipost.org/SciPostPhys.14.6.141
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 14
IS  - 6
SP  - 141
A1  - Huang, Jin-Long
AU  - McGreevy, John
AU  - Shi, Bowen
AB  - We extend the entanglement bootstrap program 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 [Ann. Phys. 418, 168164
(2020), Phys. Rev. B 103, 115150 (2021)], 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.
ER  -

@Article{10.21468/SciPostPhys.14.6.141,
	title={{Knots and entanglement}},
	author={Jin-Long Huang and  John McGreevy and Bowen Shi},
	journal={SciPost Phys.},
	volume={14},
	pages={141},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.14.6.141},
	url={https://scipost.org/10.21468/SciPostPhys.14.6.141},
}