Geometric phases for mixed states of the Kitaev chain

The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyse the intricate behaviour of Uhlmann&#...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2016-05, Vol.374 (2068), p.20150231
Main Authors: Andersson, Ole, Bengtsson, Ingemar, Ericsson, Marie, Sjöqvist, Erik
Format: Article
Language:English
Subjects:
Fermions
Fysik
Fysik med inriktning mot atom- molekyl- och kondenserande materiens fysik
geometric phase
Interferometric Phase
Kitaev Chain
Physics
Physics with spec. in Atomic, Molecular and Condensed Matter Physics
thermal states
Uhlmann Phase
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Summary:The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyse the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyse the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation.
ISSN:1364-503X
1471-2962
1471-2962
DOI:10.1098/rsta.2015.0231