Two-dimensional density-matrix topological fermionic phases: topological Uhlmann numbers



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Viyuela García, Óscar and Rivas Vargas, Ángel and Martin-Delgado Alcántara, Miguel Ángel (2014) Two-dimensional density-matrix topological fermionic phases: topological Uhlmann numbers. Physical review letters, 113 (7). ISSN 0031-9007

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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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© 2014 American Physical Society. We are thankful for the following: the Spanish MINECO Grants No. FIS2012-33152 and No. FIS2009-10061, the CAM research consortium QUITEMAD S2009-ESP-1594, the European Commission PICC: FP7 2007-2013, Grant No. 249958, the UCM-BS Grant No. GICC-910758, and the FPU MEC Grant and Residencia de Estudiantes.

Uncontrolled Keywords:Superconductors; States; Insulators; computation; Degeneracy; Statistics; Vortices; Parity; Space; Model.
Subjects:Sciences > Physics > Physics-Mathematical models
ID Code:47307
Deposited On:04 May 2018 09:59
Last Modified:04 May 2018 17:49

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