Current density functional theory for one-dimensional fermions

摘要

The frequency-dependent response of a one-dimensionalfermion system is investigated using Current Density Func-tional Theory (CDFT) within the local approximation (LDA).DFT-LDA, and in particular CDFT-LDA, reproduces very wellthe dispersion of the collective excitations. Unsurprisingly,however, the approximation fails for details of the dynamic re-sponse for large wavevectors. In particular, we introduce CDFT for the one-dimensional spin-less fermion model with nearest-neighbor interaction, and useCDFT-LDA plus exact (Bethe ansatz) results for the ground-state energy as function of particle density and boundary phaseto determine the linear response. The su6cesses and failures ofthis approach are discussed in detail.