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.

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© 2017 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: November 22, 2016; Revised: May 28, 2017; Accepted: July 6, 2017; Published: July 14, 2017. Article funded by SCOAP3. The first author received support from the Clay Mathematical Institute, Trinity College Cambridge, and the University of Edinburgh. The second author was partially supported by NSF grants DMS-1201512 and 1707882 and PHY-1205440 and the Perimeter Institute for Theoretical Physics. The second author would also like to thank Andrew Ranicki and Ida Thompson for their generous hospitality during her visits to the first author in Edinburgh.

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Published - 10.1007_2FJHEP07_2017_076.pdf

Submitted - 1611.04047.pdf

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