Duality and topology

Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non-canonical transformations in general also change the statistics of the operators involved. In these cases one may expect a change of topological properties a...

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Bibliographic Details
Published in:Annals of physics 2018-04, Vol.391, p.216-239
Main Authors: Sacramento, P.D., Vieira, V.R.
Format: Article
Language:English
Subjects:
CANONICAL TRANSFORMATIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DUALITY
Duality operation
Majorana fermion representation
MAJORANA FERMIONS
SPECTRA
SPIN
STATISTICS
SUPERCONDUCTORS
Topological invariant
TOPOLOGY
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Summary:Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non-canonical transformations in general also change the statistics of the operators involved. In these cases one may expect a change of topological properties as a consequence of the mapping. Here we consider some dualities resulting from mappings, by systematically using a Majorana fermion representation of spin and fermionic problems. We focus on the change of topological invariants that results from unitary transformations taking as examples the mapping between a spin system and a topological superconductor, and between different fermionic systems.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2018.02.017