# Locality of Interatomic Forces in Tight Binding Models for Insulators

## TL;DR

This paper demonstrates that in insulators, the potential energy in tight binding models can be decomposed into localized site energies, providing insights into interatomic interactions and supporting multi-scale modeling.

## Contribution

It establishes exponential locality of site energy contributions in tight binding models for insulators at zero and finite temperatures, extending previous work.

## Key findings

- Potential energy decomposes into localized site energies.
- Locality estimates are uniform at finite temperature.
- Numerical tests confirm analytical locality results.

## 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 and strengthens (Chen, Ortner 2016) and (Chen, Lu, Ortner 2018) for finite temperature models.