A Time-Dependent Random State Approach for Large-scale Density Functional Calculations

TL;DR

This paper introduces a novel time-dependent random state method for large-scale density functional calculations that avoids diagonalization, offering scalable accuracy and efficiency for complex condensed matter systems.

Contribution

The authors develop a self-consistent density functional method using a time-dependent random state approach, reducing computational cost and maintaining accuracy for large systems.

Findings

Accuracy scales as 1/√(SN_e), enabling efficient large-scale calculations.

A single random state can suffice for large systems with acceptable precision.

Method validated across various condensed matter systems.

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 $1/\sqrt{SN_{e}}$, 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.