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arXiv · 1309.1174

Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems

O. Viyuela·A. Rivas·M. A. Martin-Delgado
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Abstract

We introduce the Uhlmann geometric phase as a tool to characterize symmetry-protected topological phases in 1D 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 $T_c$ 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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O. Viyuela, A. Rivas, M. A. Martin-Delgado. 2014-03-17. Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems. https://doi.org/10.1103/physrevlett.112.130401

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