A Time-Dependent Random State Approach for Large-Scale Density Functional Calculations
Weiqing Zhou and Shengjun Yuan*
Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
Abstract ：We develop a self-consistent first-principle method based on the density functional theory. Physical quantities such as the density of states, Fermi energy and electron density are obtained using a time-dependent random state method without diagonalization. The numerical error for calculating either global or local variables always scales as $1/\sqrt{SN_{\rm e}}$, where $N_{\rm e}$ is the number of electrons and $S$ is the number of random states, leading to a sublinear computational cost with the system size. In the limit of large systems, one random state could be enough to achieve reasonable accuracy. The accuracy and scaling properties of using the method are derived analytically and verified numerically in different condensed matter systems. Our time-dependent random state approach provides a powerful strategy for large-scale density functional calculations.
收稿日期: 2022-12-17
Express Letter
出版日期: 2023-02-01
:
31.15.E-
71.15.-m
(Methods of electronic structure calculations)
71.15.Mb
(Density functional theory, local density approximation, gradient and other corrections)
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2023, Vol. 40 
