Optical bounds on many-electron localization

We establish rigorous inequalities between different electronic properties linked to optical sum rules, and organize them into weak and strong bounds on three characteristic properties of insulators: electron localization length $\ell$ (the quantum fluctuations in polarization), electric susceptibil...

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Main Author: Ivo Souza, Richard M. Martin, Massimiliano Stengel
Format: Article
Language:English
Published: SciPost 2025-04-01
Series:SciPost Physics
Online Access:https://scipost.org/SciPostPhys.18.4.127
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author Ivo Souza, Richard M. Martin, Massimiliano Stengel
author_facet Ivo Souza, Richard M. Martin, Massimiliano Stengel
author_sort Ivo Souza, Richard M. Martin, Massimiliano Stengel
collection DOAJ
description We establish rigorous inequalities between different electronic properties linked to optical sum rules, and organize them into weak and strong bounds on three characteristic properties of insulators: electron localization length $\ell$ (the quantum fluctuations in polarization), electric susceptibility $\chi$, and optical gap $E_{\mathrm{G}}$. All-electron and valence-only versions of the bounds are given, and the latter are found to be more informative. The bounds on $\ell$ are particularly interesting, as they provide reasonably tight estimates for an ellusive ground-state property – the average localization length of valence electrons – from tabulated experimental data: electron density, high-frequency dielectric constant, and optical gap. The localization lengths estimated in this way for several materials follow simple chemical trends, especially for the alkali halides. We also illustrate our findings via analytically solvable harmonic oscillator models, which reveal an intriguing connection to the physics of long-ranged van der Waals forces.
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spelling doaj-art-b7e8c0ffa82142bb874cd5e44cd778522025-08-20T02:12:35ZengSciPostSciPost Physics2542-46532025-04-0118412710.21468/SciPostPhys.18.4.127Optical bounds on many-electron localizationIvo Souza, Richard M. Martin, Massimiliano StengelWe establish rigorous inequalities between different electronic properties linked to optical sum rules, and organize them into weak and strong bounds on three characteristic properties of insulators: electron localization length $\ell$ (the quantum fluctuations in polarization), electric susceptibility $\chi$, and optical gap $E_{\mathrm{G}}$. All-electron and valence-only versions of the bounds are given, and the latter are found to be more informative. The bounds on $\ell$ are particularly interesting, as they provide reasonably tight estimates for an ellusive ground-state property – the average localization length of valence electrons – from tabulated experimental data: electron density, high-frequency dielectric constant, and optical gap. The localization lengths estimated in this way for several materials follow simple chemical trends, especially for the alkali halides. We also illustrate our findings via analytically solvable harmonic oscillator models, which reveal an intriguing connection to the physics of long-ranged van der Waals forces.https://scipost.org/SciPostPhys.18.4.127
spellingShingle Ivo Souza, Richard M. Martin, Massimiliano Stengel
Optical bounds on many-electron localization
SciPost Physics
title Optical bounds on many-electron localization
title_full Optical bounds on many-electron localization
title_fullStr Optical bounds on many-electron localization
title_full_unstemmed Optical bounds on many-electron localization
title_short Optical bounds on many-electron localization
title_sort optical bounds on many electron localization
url https://scipost.org/SciPostPhys.18.4.127
work_keys_str_mv AT ivosouzarichardmmartinmassimilianostengel opticalboundsonmanyelectronlocalization