Low complexity method for large-scale self-consistent ab initio electronic-structure calculations without localization

A low-complexity method to perform self-consistent electronic structure calculations using the Kohn-Sham formalism of density functional theory is presented. Localization constraints are neither imposed nor required, thereby allowing direct comparison with conventional cubically scaling algorithms. To our knowledge, the method has, to date, the lowest complexity of any algorithm for an exact calculation. A simple one-dimensional model system is used to thoroughly test the numerical stability of the algorithm and results for real physical systems are also given.