The tight binding model is a minimalistic electronic structure model for predicting properties of materials and molecules. For insulators at zero Fermi-temperature we show that the potential energy surface of this model can be decomposed into exponentially localised site energy contributions, thus providing qualitatively sharp estimates on the interatomic interaction range which justifies a range of multi-scale models. For insulators at finite Fermi-temperature we obtain locality estimates that are uniform in the zero-temperature limit. A particular feature of all our results is that they depend only weakly on the point spectrum. Numerical tests confirm our analytical results. This work extends Chen and Ortner [Multiscale Model. Simul. 14 (2016) 232–264] and Chen et al. [Arch. Ration. Mech. Anal. 230 (2018) 701–733] to the case of zero Fermi-temperature as well as strengthening the results proved therein.
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Publié le :
DOI : 10.1051/m2an/2020020
Mots-clés : Strong locality, tight binding, point defects
@article{M2AN_2020__54_6_2295_0,
author = {Ortner, Christoph and Thomas, Jack and Chen, Huajie},
title = {Locality of interatomic forces in tight binding models for insulators},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2295--2318},
publisher = {EDP-Sciences},
volume = {54},
number = {6},
year = {2020},
doi = {10.1051/m2an/2020020},
mrnumber = {4173148},
zbl = {1466.74003},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2020020/}
}
TY - JOUR AU - Ortner, Christoph AU - Thomas, Jack AU - Chen, Huajie TI - Locality of interatomic forces in tight binding models for insulators JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2020 SP - 2295 EP - 2318 VL - 54 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2020020/ DO - 10.1051/m2an/2020020 LA - en ID - M2AN_2020__54_6_2295_0 ER -
%0 Journal Article %A Ortner, Christoph %A Thomas, Jack %A Chen, Huajie %T Locality of interatomic forces in tight binding models for insulators %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2020 %P 2295-2318 %V 54 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2020020/ %R 10.1051/m2an/2020020 %G en %F M2AN_2020__54_6_2295_0
Ortner, Christoph; Thomas, Jack; Chen, Huajie. Locality of interatomic forces in tight binding models for insulators. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 6, pp. 2295-2318. doi : 10.1051/m2an/2020020. http://www.numdam.org/articles/10.1051/m2an/2020020/
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