Anyons in geometric models of matter

Abstract

We show that the "geometric models of matter" approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold singularities along embedded 2-dimensional surfaces. The anyon states arise through the braid representation of surface braids wrapped around the orbifold singularities, coming from multisections of the orbifold normal bundle of the embedded surface. We show that the resulting braid representations can give rise to a universal quantum computer.

Quantum Computing, Seifert Surfaces, and Singular Fibers

“…There exists surface braids wrapped around singularities within 4-manifolds that support quasiparticles closely related to anyon states [30]. More work is necessary to connect our observations to this latter work.…”