title: Topological indices for open and thermal systems via Uhlmann's phase.
abstract: Two-dimensional topological phases are characterized by Thouless-Kohmoto-Nightingale-den Nijs integers, which classify Bloch energy bands or groups of Bloch bands. However, quantization does not survive thermal averaging or dephasing to mixed states. We show that using Uhlmann's parallel transport for density matrices [Rep. Math. Phys. 24, 229 (1986).
authors.affiliation: Department of Physics, University of California, San Diego, California 92093, USA.
authors.forename: Zhoushen
authors.initials: Z
authors.lastname: Huang
authors.affiliation: Department of Physics, University of California, San Diego, California 92093, USA.
authors.forename: Daniel P
authors.initials: DP
authors.lastname: Arovas