Abstract
We report a linear-scaling random Green's function(rGF)method for large-scale electronic structure calcu-lation.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=0K can reach an error of～1meV per H2O molecule in total energy,compared to deterministic calculations.The rGF method provides an effective stochastic method for large-scale electronic structure simulation.
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