title: Geometric phases for mixed states of the Kitaev chain.
abstract: 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.
authors.affiliation: Department of Physics, Stockholm University, 106 91 Stockholm, Sweden.
authors.forename: Ole
authors.initials: O
authors.lastname: Andersson
authors.affiliation: Department of Physics, Stockholm University, 106 91 Stockholm, Sweden ingemar.bengtsson@fysik.su.se.
authors.forename: Ingemar
authors.identifier: http://orcid.org/0000-0002-4203-3180
authors.initials: I
authors.lastname: Bengtsson
authors.affiliation: Department of Quantum Chemistry, Uppsala University, Box 518, 751 20 Uppsala, Sweden Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden.
authors.forename: Marie
authors.initials: M
authors.lastname: Ericsson
authors.affiliation: Department of Quantum Chemistry, Uppsala University, Box 518, 751 20 Uppsala, Sweden Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden.
authors.forename: Erik
authors.initials: E
authors.lastname: Sjöqvist
keywords: Kitaev chain; Uhlmann phase; interferometric phase