Total energy electronic structure calculations, based on density functional
theory or on the more empirical tight binding approach, are generally believed
to scale as the cube of the number of electrons. By using the localisaton
property of the high temperature density matrix we present exact deterministic
algorithms that scale linearly in one dimension and quadratically in all
others. We also introduce a stochastic algorithm that scales linearly with
system size. These results hold for metallic and non metallic systems and are
substantiated by numerical calculations on model systems.Comment: 9 pages, 2 figure