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Mixed-state topological order parameters for symmetry-protected fermion matter

Ze-Min Huang1,2 and Sebastian Diehl1

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Phys. Rev. Research 7, 033028 – Published 7 July, 2025

DOI: https://doi.org/10.1103/h1qg-96kw

Abstract

We construct an observable mixed-state topological order parameter for symmetry-protected free-fermion matter. It resolves the entire table of topological insulators and superconductors, relying exclusively on the symmetry class, but not on unitary symmetries. It provides a robust, quantized signal not only for pure ground states, but also for mixed states in or out of thermal equilibrium. Key ingredient is a unitary probe operator, whose phase can be related to spectral asymmetry, in turn revealing the topological properties of the underlying state. This is demonstrated analytically in the continuum limit, and validated numerically on the lattice. The order parameter is experimentally accessible via either interferometry or full counting statistics, for example, in cold-atom experiments.

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Phys. Rev. Research 7, 033028– Published 7 July, 2025
  • Received 5 February 2024
  • Revised 5 March 2025
  • Accepted 29 May 2025
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