Current Density Functional Theory for one-dimensional fermions

TL;DR

This paper applies Current Density Functional Theory within the local approximation to analyze the dynamic response of one-dimensional fermion systems, successfully capturing collective excitations but with limitations at large wavevectors.

Contribution

It introduces CDFT for 1D spinless fermions with nearest-neighbor interaction and compares CDFT-LDA results with exact Bethe ansatz data.

Findings

CDFT-LDA accurately reproduces collective excitation dispersion.

Fails to capture detailed responses at large wavevectors.

Combines CDFT with Bethe ansatz for groundstate energy analysis.

Abstract

The frequency-dependent response of a one-dimensional fermion system is investigated using Current Density Functional Theory (CDFT) within the local approximation (LDA). DFT-LDA, and in particular CDFT-LDA, reproduces very well the dispersion of the collective excitations. Unsurprisingly, however, the approximation fails for details of the dynamic response for large wavevectors. In particular, we introduce CDFT for the one-dimensional spinless fermion model with nearest-neighbor interaction, and use CDFT-LDA plus exact (Bethe ansatz) results for the groundstate energy as function of particle density and boundary phase to determine the linear response. The successes and failures of this approach are discussed in detail.