Chern number and Berry curvature for Gaussian mixed states of fermions

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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Cited by in corpus (5)

• Many-Body Open Quantum Systems
• Topological phase transitions at finite temperature
• Symmetry-Preserving Quadratic Lindbladian and Dissipation Driven Topological Transitions in Gaussian States
• ${\mathbb{Z}}_2$ topological invariants for mixed states of fermions in time-reversal invariant band structures
• Proxy ensemble geometric phase and proxy index of time-reversal invariant topological insulators at finite temperatures