Random Green's Function Method for Large-Scale Electronic Structure Calculation

We report a linear-scaling random Green's function (rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states and is efficiently calculated by projecting onto Krylov subspace. With the rGF method, the Fermi-Dirac operator can be obtained directly, avoiding the polynomial expansion to Fermi-Dirac function. To demonstrate the applicability, we implement the rGF method with the density-functional tight-binding method. It is shown that the Krylov subspace can maintain at small size for materials with different gaps at zero temperature, including H2O and Si clusters. We find with a simple deflation technique that the rGF self-consistent calculation of H2O clusters at T = 0 K can reach an error of similar to 1 meV per H2O molecule in total energy, compared to deterministic calculations. The rGF method provides an effective stochastic method for large-scale electronic structure simulation.