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The Quantum Double Model with Boundary: Condensations and Symmetries
Open accessAbstract
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 S3 (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.
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Citations
Cites
Anyons in an exactly solved model and beyond
Kitaev, A. (2006) · Annals of Physics · doi:10.1016/j.aop.2005.10.005 · Cited by 5,245
Quantum codes on a lattice with boundary
Bravyi, S. B., & Kitaev, A. Y. (1998) · arXiv · doi:10.48550/arxiv.quant-ph/9811052 · Cited by 394
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Barkeshli, M., Bonderson, P., Cheng, M., & Wang, Z. (2019) · Physical Review B · doi:10.1103/physrevb.100.115147 · Cited by 533
Twist defects and projective non-Abelian braiding statistics
Barkeshli, M., Jian, C.-M., & Qi, X.-L. (2013) · Physical Review B · doi:10.1103/physrevb.87.045130 · Cited by 275
Metadata
- Authors
- Beigi, S., Shor, P. W., & Whalen, D.
- Venue
- Communications in Mathematical Physics
- Published
- 2011-06-28
- Volume
- 306
- Issue
- 3
- Pages
- 663-694
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W2131970804
- Cited by
- 234
- References
- 2
- FWCI
- 3.82
- Type
- journal article
- Language
- en
- Open access
- green
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- Beigi, S., Shor, P. W., & Whalen, D. (2011). The Quantum Double Model with Boundary: Condensations and Symmetries. Communications in Mathematical Physics. https://doi.org/10.1007/s00220-011-1294-x
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