Canonical purification of the density matrix in electronic-structure theory

Two methods are suggested for performing ground-state electronic-structure calculations within the independent-electron approximation. Both methods involve the purification of a specified initial density matrix, which can be done either canonically (at a fixed electron count $N_e)$ or grand canonically (at a fixed chemical potential μ). Linear system-size scaling is achieved either way, as we illustrate in example tight-binding calculations on carbon nanotubes.