title: Uhlmann phase as a topological measure for one-dimensional fermion systems.
abstract: We introduce the Uhlmann geometric phase as a tool to characterize symmetry-protected topological phases in one-dimensional fermion systems, such as topological insulators and superconductors. Since this phase is formulated for general mixed quantum states, it provides a way to extend topological properties to finite temperature situations. We illustrate these ideas with some paradigmatic models and find that there exists a critical temperature Tc at which the Uhlmann phase goes discontinuously and abruptly to zero. This stands as a borderline between two different topological phases as a function of the temperature. Furthermore, at small temperatures we recover the usual notion of topological phase in fermion systems.
authors.affiliation: Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain.
authors.forename: O
authors.initials: O
authors.lastname: Viyuela
authors.affiliation: Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain.
authors.forename: A
authors.initials: A
authors.lastname: Rivas
authors.affiliation: Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain.
authors.forename: M A
authors.initials: MA
authors.lastname: Martin-Delgado