%0 Journal Article
%A Viyuela García, Óscar
%A Rivas Vargas, Ángel
%A Martín-Delgado Alcántara, Miguel Ángel
%T Two-dimensional density-matrix topological fermionic phases: topological Uhlmann numbers
%D 2014
%@ 0031-9007
%U https://hdl.handle.net/20.500.14352/35592
%X We construct a topological invariant that classifies density matrices of symmetry-protected topological orders in two-dimensional fermionic systems. As it is constructed out of the previously introduced Uhlmann phase, we refer to it as the topological Uhlmann number n_(U). With it, we study thermal topological phases in several two-dimensional models of topological insulators and superconductors, computing phase diagrams where the temperature T is on an equal footing with the coupling constants in the Hamiltonian. Moreover, we find novel thermal-topological transitions between two nontrivial phases in a model with high Chern numbers. At small temperatures we recover the standard topological phases as the Uhlmann number approaches to the Chern number.
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