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arXiv · 2512.21843

The Loring--Schulz-Baldes Spectral Localizer Revisited

Gregory Berkolaiko·Jacob Shapiro·Beyer Chase White
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Abstract

The spectral localizer, introduced by Loring in 2015 and Loring and Schulz-Baldes in 2017, is a method to compute the (infinite volume) topological invariant of a quantum Hamiltonian on $\ZZ^d$, as the signature of the (finite) localizer matrix. We present a direct and elementary spectral-theoretic proof treating the $d=1$ and $d=2$ cases on an almost equal footing. Moreover, we re-interpret the localizer as a higher-dimensional topological insulator via the bulk-edge correspondence.

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Gregory Berkolaiko, Jacob Shapiro, Beyer Chase White. 2025-12-26. The Loring--Schulz-Baldes Spectral Localizer Revisited. https://arxiv.org/abs/2512.21843

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