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arXiv · 2104.12115

Chern number and Berry curvature for Gaussian mixed states of fermions

Lukas Wawer·Michael Fleischhauer
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Abstract

We generalize the concept of topological invariants for mixed states based on the ensemble geometric phase (EGP) introduced for one-dimensional lattice models to two dimensions. In contrast to the geometric phase for density matrices suggested by Uhlmann, the EGP leads a proper Chern number for Gaussian, finite-temperature or non-equilibrium steady states. The Chern number can be expressed as an integral of the Berry curvature of the so-called fictitious Hamiltonian, constructed from single-particle correlations, over the two-dimensional Brillouin zone. For the Chern number to be non-zero the fictitious Hamiltonian has to break time-reversal symmetry.

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Lukas Wawer, Michael Fleischhauer. 2021-04-25. Chern number and Berry curvature for Gaussian mixed states of fermions. https://doi.org/10.1103/physrevb.104.094104

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