The Loring--Schulz-Baldes Spectral Localizer Revisited
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909976072552448 |
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| author | Berkolaiko, Gregory Shapiro, Jacob White, Beyer Chase |
| author_facet | Berkolaiko, Gregory Shapiro, Jacob White, Beyer Chase |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21843 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Loring--Schulz-Baldes Spectral Localizer Revisited Berkolaiko, Gregory Shapiro, Jacob White, Beyer Chase Mathematical Physics Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics Functional Analysis Quantum Physics 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. |
| title | The Loring--Schulz-Baldes Spectral Localizer Revisited |
| topic | Mathematical Physics Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics Functional Analysis Quantum Physics |
| url | https://arxiv.org/abs/2512.21843 |