An Efficient Algorithm for Density Functional Theory Simulation of Large Quantum Dot Systems

TL;DR

This paper introduces a new computational algorithm that significantly improves the efficiency of simulating large quantum dot systems using density functional theory, enabling studies of systems with hundreds of electrons.

Contribution

The paper presents a novel algorithm combining particle-in-the-box, conjugate gradient, Fourier convolution, and multi-grid techniques for efficient large-scale quantum dot simulations.

Findings

Enables simulation of quantum dots with hundreds of electrons

Reduces computational cost compared to previous methods

Demonstrates effectiveness on a 2D model system

Abstract

Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. An efficient algorithm for the density-functional theory simulation of quantum dots is developed, which includes the particle-in-the-box representation of the Kohn-Sham orbitals, an efficient conjugate gradient method to directly minimize the total energy, a Fourier convolution approach for the calculation of the Hartree potential, and a simplified multi-grid technique to accelerate the convergence. The new algorithm is tested in a 2D model system. Using this new algorithm, numerical studies of large quantum dots with several hundred electrons become computationally affordable.