Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model
Non-Abelian statistics is a phenomenon of topologically protected non-Abelian geometric phases as we exchange quasiparticle excitations. Here we construct a Z[subscript N] rotor model that realizes a self-dual Z[subscript N] Abelian gauge theory. We find that lattice dislocation defects in the model...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2013
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| Online Access: | http://hdl.handle.net/1721.1/75856 https://orcid.org/0000-0002-5874-581X |
| Summary: | Non-Abelian statistics is a phenomenon of topologically protected non-Abelian geometric phases as we exchange quasiparticle excitations. Here we construct a Z[subscript N] rotor model that realizes a self-dual Z[subscript N] Abelian gauge theory. We find that lattice dislocation defects in the model produce topologically protected degeneracy. Even though dislocations are not quasiparticle excitations, they resemble non-Abelian anyons with quantum dimension √N. Exchanging dislocations can produce topologically protected projective non-Abelian geometric phases. Therefore, we discover a kind of (projective) non-Abelian anyon that appears as the dislocations in an Abelian Z[subscript N] rotor model. These types of non-Abelian anyons can be viewed as a generalization of the Majorana zero modes. |
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