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The Loring--Schulz-Baldes Spectral Localizer Revisited
Published 26 Dec 2025 in math-ph, cond-mat.dis-nn, cond-mat.mes-hall, math.FA, and quant-ph | (2512.21843v1)
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 $\ZZd$, 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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