A gradient flow model for ground state calculations in Wigner formalism based on density functional theory

TL;DR

This paper introduces a gradient flow model based on density functional theory to efficiently compute ground state Wigner functions for many-body systems, enabling large-scale simulations with high accuracy.

Contribution

It proposes a novel energy functional in Wigner formalism and develops an efficient algorithm with spectral methods for ground state calculations.

Findings

Accurate ground state Wigner functions for large systems

Algorithm complexity is $O(n_{DoF}\log n_{DoF})$ per iteration

Successful simulations of 1D and 3D systems with defects

Abstract

In this paper, a gradient flow model is proposed for conducting ground state calculations in Wigner formalism of many-body system in the framework of density functional theory. More specifically, an energy functional for the ground state in Wigner formalism is proposed to provide a new perspective for ground state calculations of the Wigner function. Employing density functional theory, a gradient flow model is designed based on the energy functional to obtain the ground state Wigner function representing the whole many-body system. Subsequently, an efficient algorithm is developed using the operator splitting method and the Fourier spectral collocation method, whose numerical complexity of single iteration is $O(n_{\rm DoF}\log n_{\rm DoF})$. Numerical experiments demonstrate the anticipated accuracy, encompassing the one-dimensional system with up to $2^{21}$ particles and the three-dimensional system with defect, showcasing the potential of our approach to large-scale simulations and computations of systems with defect.