Rigorous body-order approximations of an electronic structure potential energy landscape

TL;DR

This paper demonstrates that the local density of states in certain tight-binding models can be expanded in a body-order series with exponential convergence, impacting electronic structure modeling.

Contribution

It proves the exponential convergence of body-order expansions for analytic observables in a broad class of tight-binding models.

Findings

Exponential convergence of body-order expansion for LDOS

Applicable to finite Fermi-temperature and insulators

Implications for potential energy landscape modeling

Abstract

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.