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Entanglement Theory Quantum Correlations
The Loring--Schulz-Baldes Spectral Localizer Revisited
arXiv
Authors: Gregory Berkolaiko, Jacob Shapiro, Beyer Chase White
Year
2025
Paper ID
36220
Status
Preprint
Abstract Read
~2 min
Abstract Words
70
Citations
N/A
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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- 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...
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