Communications in Mathematical Physics

, Volume 306, Issue 3, pp 663–694 | Cite as

The Quantum Double Model with Boundary: Condensations and Symmetries

  • Salman Beigi
  • Peter W. Shor
  • Daniel Whalen


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.


Domain Wall Irreducible Representation Conjugacy Class Vertex Operator Fusion Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institute for Quantum InformationCalifornia Institute of TechnologyPasadenaUSA
  2. 2.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  3. 3.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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