Anyons in Geometric Models of Matter

Creators: Atiyah, Michael; Marcolli, Matilde

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.

Additional Information

© 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.

Attached Files

Published - 10.1007_2FJHEP07_2017_076.pdf

Submitted - 1611.04047.pdf

Files

10.1007_2FJHEP07_2017_076.pdf

Files (717.3 kB)

Name	Size	Download all
10.1007_2FJHEP07_2017_076.pdf md5:9cf0dc87f4763fe112a3a4391a867890	447.6 kB	Preview Download
1611.04047.pdf md5:6952a895423b2d201e9acf54bc103863	269.7 kB	Preview Download

Additional details

	All versions	This version
Views	0	0
Downloads	0	0
Data volume	0 Bytes	0 Bytes