大规模密度泛函计算的含时随机态方法
A Time-Dependent Random State Approach for Large-scale Density Functional Calculations
摘要：
我们发展了一种基于密度泛函理论的自洽第一性原理方法。采用不对角化的含时随机态方法，得到了态密度、费米能和电子密度等物理量。用于计算全局或局部变量的数值误差总是按$1/\sqrt{SN_{e}}$缩放，其中$N_{e}$是电子的数量，而$S$是随机状态的数量，导致计算成本与系统大小呈次线性关系。在大系统的极限下，一个随机状态就足以达到合理的精度。该方法的准确性和标度特性的解析推导和数值验证在不同的凝聚态系统。我们的含时随机态方法为大规模密度泛函计算提供了一个强有力的策略。
英文摘要：
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 $1/\sqrt{SN_{e}}$, where $N_{e}$ 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 method's accuracy and scaling properties 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.
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