Chern number and Berry curvature for Gaussian mixed states of fermions
2021
We generalize the concept of topological invariants for mixed states based on the ensemble geometric phase (EGP) to two-dimensional band structures. In contrast to the geometric Uhlmann phase for density matrices, the EGP leads to a proper Chern number for Gaussian, finite-temperature, or nonequilibrium steady states. The Chern number can be expressed as an integral of the ground-state Berry curvature of a fictitious lattice Hamiltonian, constructed from single-particle correlations. For the Chern number to be nonzero the fictitious Hamiltonian has to break time-reversal symmetry.
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