Anyons in Geometric Models of Matter

TL;DR

This paper demonstrates how geometric models of matter can be used to construct anyon quasiparticles with fractional quantum numbers via 4D orbifold geometries, enabling potential quantum computing applications.

Contribution

It introduces a novel geometric framework for modeling anyons using 4D edge-cone orbifold geometries with embedded surfaces, linking topology to quantum computation.

Findings

Construction of anyon models using orbifold geometries

Braid representations from surface braids encode quantum information

Potential for universal quantum computation using these models

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.