  We show that the local density of states (LDOS) of a wide class of
tight-binding models has a weak body-order expansion. Specifically, we prove
that the resulting body-order expansion for analytic observables such as the
electron density or the energy has an exponential rate of convergence both at
finite Fermi-temperature as well as for insulators at zero Fermi-temperature.
We discuss potential consequences of this observation for modelling the
potential energy landscape, as well as for solving the electronic structure
problem.
