Lukas Wawer, Michael Fleischhauer:
Phys. Rev. B 104, 214107 (2021)
🔓 arXiv:2109.01487 (2021)
The topological classification of fermion systems in mixed states is a long standing quest. For Gaussian states, reminiscent of non-interacting unitary fermions, some progress has been made. While the topological quantization of certain observables such as the Hall conductivity is lost for mixed states, directly observable many-body correlators exist which preserve the quantized nature and naturally connect to known topological invariants in the ground state. For systems which break time-reversal (TR) symmetry, the ensemble geometric phase was identified as such an observable which can be used to define a Chern number in (1+1) and 2 dimensions. Here we propose a corresponding Z2 topological invariant for systems with TR symmetry. We show that this mixed-state invariant is identical to well-known Z2 invariants for the ground state of the so-called fictitious Hamiltonian, which for thermal states is just the ground state of the system Hamiltonian itself. We illustrate our findings for finite-temperature states of a paradigmatic Z2 topological insulator, the Kane-Mele model.