Reduce Noise in Stochastic Density Functional Theory

Large scale density functional theory (DFT) calculations are necessary for understanding the physics of complex materials. Steep numerical scaling of conventional DFT methods prohibits the routine application to large systems containing tens of thousands of electrons. An alternative to conventional DFT is based on representing the density and density matrix using stochastic sampling of the occupied subspace, allowing for linear or even sub-linear scaling DFT method at the cost of introducing a well-controlled statistical error. It becomes an important task to develop approaches that reduce the stochastic noise in order to improve accuracy and reliability of stochastic DFT. Two different noise reduction techniques have been introduced in stochastic DFT. One is based on decomposing the system into overlapped fragments and the other approach divides the occupied subspace into subspaces according to energy windows. Both noise reduction techniques can significantly reduce the noise level in electronic structures, which leads to orders of magnitude reduction in computational costs. This talk will provide a look into both methods including analysis of noise reduction, scaling, and performance. Illustrations will be given for semiconductor materials with nearly 16,000 electrons.