2014/05/31 by O. Viyuela, Oscar Viyuela, A. Rivas +3 · 4 citations
Materials Science · Mathematics · Physics and Astronomy · #Combinatorics #Graphene research and applications #Hamiltonian (control theory) #Invariant (physics) #Mathematics #Physics #Pure mathematics #Quantum many-body systems #Quantum mechanics #Symmetry protected topological order #Topological Materials and Phenomena #Topological degeneracy #Topological entropy in physics #Topological insulator #Topological order #Topological quantum number #Topological ring #Topological space #Topological vector space #Topology (electrical circuits) #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevlett.113.076408
published as Phys. Rev. Lett. 113, 076408 (2014) · RevTex4 file, color figures. Close to published version
openalex publication_date 2014/08/13 · arxiv created 2014/08/25 · arxiv updated 2014/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 nU. 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.