What the study found
The study explicitly demonstrates that the spectral localizer is equivalent to local Chern and winding markers. The authors show that Chern and winding markers appear as leading-order terms in a perturbative expansion in the spectral localizer parameter κ.
Why the authors say this matters
The authors say this matters because the result makes the connection between these real-space topological invariants explicit. They conclude that the approach bypasses abstract topological machinery and may be accessible to a broader physics audience.
What the researchers tested
The researchers examined topological invariants used for band insulators, especially in systems without translational symmetry such as disordered, quasicrystalline, or amorphous systems. They used a systematic perturbative expansion in powers of the spectral localizer’s parameter κ and relied only on the Clifford algebra of the spectral localizer.
What worked and what didn't
Their expansion showed that the Chern marker and the winding marker emerge as leading-order terms. The abstract states that this provides an explicit equivalence with the spectral localizer. It does not describe any failed cases or exceptions.
What to keep in mind
The abstract does not provide detailed limitations, numerical tests, or conditions under which the equivalence might fail. It also does not describe specific models beyond the general setting of systems lacking translational symmetry.
Key points
- The paper states an explicit equivalence between the spectral localizer and local Chern and winding markers.
- Chern and winding markers arise as leading-order terms in an expansion in the spectral localizer parameter κ.
- The derivation uses a systematic perturbative expansion and only the Clifford algebra of the spectral localizer.
- The authors say the approach bypasses abstract topological machinery and may be accessible to a broader physics audience.
- The abstract does not describe specific limitations or exceptions.
Disclosure
- Research title:
- Spectral localizer matches local Chern and winding markers
- Authors:
- Lucien Jezequel, Jens H. Bardarson, Adolfo G. Grushin
- Institutions:
- KTH Royal Institute of Technology, Institut polytechnique de Grenoble, Ikerbasque, Institut Néel, Donostia International Physics Center, Université Grenoble Alpes
- Publication date:
- 2026-04-28
- OpenAlex record:
- View
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