What the study found
The study finds an explicit equivalence between the spectral localizer and the local Chern and winding markers. It shows that the local Chern marker and winding marker appear as leading-order terms in a perturbative expansion in the spectral localizer parameter kappa.
Why the authors say this matters
The authors say this matters because topological band insulators with translational symmetry are usually classified by momentum-space topological invariants, while systems without translation symmetry need real-space definitions. The study suggests this equivalence provides a simpler approach that bypasses abstract topological machinery and may be accessible to a broader physics audience.
What the researchers tested
The researchers carried out a systematic perturbative expansion in powers of the spectral localizer's parameter kappa. They used only the Clifford algebra of the spectral localizer to compare it with the local Chern marker and winding marker.
What worked and what didn't
The expansion showed that the Chern and winding markers emerge as leading-order terms. The abstract does not describe any failed cases, counterexamples, or limits where the equivalence does not hold.
What to keep in mind
The summary provided here is limited to the abstract, so details of the proof, assumptions, and scope are not fully described. The abstract does not state specific limitations or conditions beyond the use of a perturbative expansion in kappa.
Key points
- The paper states an explicit equivalence between the spectral localizer and local Chern and winding markers.
- The local Chern and winding markers appear as leading-order terms in an expansion in the spectral localizer parameter kappa.
- The authors use only the Clifford algebra of the spectral localizer in their argument.
- The work is framed as relevant to systems without translational symmetry, such as disordered, quasicrystalline, or amorphous topological systems.
- The abstract says the approach bypasses abstract topological machinery.
Disclosure
- Research title:
- Spectral localizer matches local Chern and winding markers
- Authors:
- Lucien Jezequel, Jens H. Bardarson, Adolfo G. Grushin
- Institutions:
- Donostia International Physics Center, Ikerbasque, Institut Néel, Institut polytechnique de Grenoble, KTH Royal Institute of Technology, KTH Royal Institute of Technology, Université Grenoble Alpes
- Publication date:
- 2026-04-28
- OpenAlex record:
- View
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