Density functional theory beyond the linear regime: Validating adiabatic LDA

TL;DR

This paper develops and validates a local density approximation for 1D systems interacting via soft-Coulomb potential, demonstrating its accuracy for ground-state energies, ionization potentials, and time-dependent responses, with implications for 3D LDA.

Contribution

The paper introduces a 1D LDA based on quantum Monte-Carlo data, showing it matches exact results and can inform 3D LDA improvements and applications in strong laser field modeling.

Findings

1D LDA achieves high accuracy for ground-state energies and ionization potentials.

Time-dependent responses with 1D LDA closely match exact solutions, except for missing double excitations.

3D LDA is expected to perform well beyond linear response, supported by 1D results.

Abstract

We present a local density approximation (LDA) for one-dimensional (1D) systems interacting via the soft-Coulomb interaction based on quantum Monte-Carlo calculations. Results for the ground-state energies and ionization potentials of finite 1D systems show excellent agreement with exact calculations, obtained by exploiting the mapping of an $N$-electron system in $d$ dimensions, onto a single electron in $N\times d$ dimensions properly symmetrized by the Young diagrams. We conclude that 1D LDA is of the same quality as its three-dimensional (3D) counterpart, and we infer conclusions about 3D LDA. The linear and non-linear time-dependent responses of 1D model systems using LDA, exact exchange, and the exact solution are investigated and show very good agreement in both cases, except for the well known problem of missing double excitations. Consequently, the 3D LDA is expected to be of good quality beyond linear response. In addition, the 1D LDA should prove useful in modeling the interaction of atoms with strong laser fields, where this specific 1D model is often used.