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.

22 pages LaTeX

References in corpus (12)

• A short introduction to Fibonacci anyon models
• Skyrmions from Instantons inside Domain Walls
• Simulation of anyons with tensor network algorithms
• Quantum Hall Systems: Braid groups, composite fermions, and fractional charge
• Topological triviality of smoothly knotted surfaces in 4-manifolds
• Time evolution in a geometric model of a particle
• The structure of fixed-point tensor network states characterizes patterns of long-range entanglement
• Geometric Models of Helium
• Projective planes, Severi varieties and spheres
• The Non-Existent Complex 6-Sphere
• Local unitary representations of the braid group and their applications to quantum computing
• Complex Geometry of Nuclei and Atoms

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