title: Two-dimensional density-matrix topological fermionic phases: topological Uhlmann numbers.
abstract: 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.
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