Density-matrix electronic-structure method with linear system-size scaling

We introduce a method for the solution of the electronic-structure problem in the independent-electron approximation. The method is based upon a variational solution for the density matrix, which is truncated to zero beyond a real-space radius ${\mathit{R}}_{\mathit{c}}$, and becomes exact as ${\mathit{R}}_{\mathit{c}}$→∞. Most importantly, the computer time scales only linearly with system size. The method is tested in the context of tight-binding models in one and three dimensions.