Z2 topological invariants for mixed states of fermions in time-reversal invariant band structures
Wawer L, Fleischhauer M (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 104
Article Number: 214107
Journal Issue: 21
DOI: 10.1103/PhysRevB.104.214107
Abstract
The topological classification of fermion systems in mixed states is a long-standing quest. For Gaussian states, reminiscent of noninteracting 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 that 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 two 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.
Involved external institutions
Germany (DE)How to cite
APA:
Wawer, L., & Fleischhauer, M. (2021). Z2 topological invariants for mixed states of fermions in time-reversal invariant band structures. Physical Review B, 104(21). https://dx.doi.org/10.1103/PhysRevB.104.214107
MLA:
Wawer, Lukas, and Michael Fleischhauer. "Z2 topological invariants for mixed states of fermions in time-reversal invariant band structures." Physical Review B 104.21 (2021).
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