The Quantum Double Model with Boundary: Condensations and Symmetries
Name
Shor_The Quantum (arxiv).pdf
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1.16 MB
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Adobe PDF
Checksum (MD5)
4246be0f4188d269c62a1b3790239df5
Author(s)
Beigi, Salman
Shor, Peter W.
Whalen, Daniel
Date Issued
June 2011
Journal
Communications in Mathematical Physics
Publisher
Springer-Verlag
Citation
Beigi, Salman, Peter W. Shor, and Daniel Whalen. “The Quantum Double Model with Boundary: Condensations and Symmetries.” Communications in Mathematical Physics 306.3 (2011): 663–694. Web.
Version
Author's final manuscript
Abstract
Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. In this paper, we define boundaries for this model and characterize condensations; that is, we find all quasi-particle excitations (anyons) which disappear when they move to the boundary. We then consider two phases of the quantum double model corresponding to two groups with a domain wall between them, and study the tunneling of anyons from one phase to the other. Using this framework we discuss the necessary and sufficient conditions when two different groups give the same anyon types. As an application we show that in the quantum double model for S 3 (the permutation group over three letters) there is a chargeon and a fluxion which are not distinguishable. This group is indeed a special case of groups of the form of the semidirect product of the additive and multiplicative groups of a finite field, for all of which we prove a similar symmetry.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00220-011-1294-x
