Detecting local topology with the spectral localizer
Abstract
The spectral localizer is a predictive framework for the computation of topological invariants of natural and artificial materials. Here, three crucial improvements on the criterion for the validity of the framework are reported: first, merely a properly defined local spectral gap of the Hamiltonian is required, second, only relative bounds on the Hamiltonian and its noncommutative derivative are relevant, and, third, the numerical constant in a tapering estimate is improved. These developments further stress the local nature of the spectral localizer framework, enabling more precise predictions in heterostructures, aperiodic, and disordered systems. Moreover, these results strengthen the bounds on the spectral localizer’s spectral flow when crossing topological phase boundaries.
Fields of Study & Subjects
Medical Imaging Techniques and Applications
Image Retrieval and Classification Techniques
Power Systems and Technologies
Publication details
- Journal / source
- ESAIM Mathematical Modelling and Numerical Analysis
- Publisher
- EDP Sciences
- Volume
- 60
- Issue
- 5
- Pages
- 2357-2383
- Publication date
- 7 August 2026
- Language
- EN