  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.
