Publication: Uhlmann phase as a topological measure for one-dimensional fermion systems
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2014-04-02
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American Physical Society
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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.
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© 2014 American Physical Society. We are grateful to the anonymous referee and to Z. Huang for pointing out a correction in a previous version of the manuscript. We thank the Spanish MINECO Grants No. FIS2012-33152 and No. FIS2009-10061, CAM research consortium QUITEMAD S2009-ESP-1594, European Commission PICC: FP7 2007-2013, Grant No. 249958, UCM-BS Grant No. GICC-910758, FPU MEC Grant and Residencia de Estudiantes.