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      Knots and entanglement

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          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, 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.

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          Author and article information

          Journal
          15 December 2021
          Article
          2112.08398
          53e931ab-54da-4cb0-8493-3f128f955c32

          http://creativecommons.org/licenses/by/4.0/

          History
          Custom metadata
          79+42 pages, 46 figures
          hep-th cond-mat.str-el quant-ph

          Condensed matter,Quantum physics & Field theory,High energy & Particle physics

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