Locality of interatomic forces in tight binding models for insulators

¹ Mathematics Institute, University of Warwick, Zeeman Building, Coventry, UK
² School of Mathematical Sciences, Beijing Normal University, Beijing, P.R. China

^* Corresponding author: J.Thomas.1@warwick.ac.uk

Received: 17 August 2019
Accepted: 24 March 2020

Abstract

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.