Successes and failures of Bethe Ansatz Density Functional Theory

TL;DR

This paper evaluates the effectiveness of Bethe Ansatz Density Functional Theory within the Local Density Approximation for one-dimensional fermion systems, highlighting its successes in capturing some collective behaviors but failures in backscattering-related properties.

Contribution

It provides a comparative analysis of DFT-LDA results against exact solutions, revealing where the approximation succeeds and fails in describing 1D fermion systems.

Findings

DFT-LDA captures low-energy excitations and collective charge dispersion

Fails to accurately describe backscattering effects and transport properties

Drude weight behavior near impurities is not well-represented

Abstract

The response of a one-dimensional fermion system is investigated using Density Functional Theory (DFT) within the Local Density Approximation (LDA), and compared with exact results. It is shown that DFT-LDA reproduces surprisingly well some of the characteristic features of the Luttinger liquid, namely the vanishing spectral weight of low energy particle-hole excitations, as well as the dispersion of the collective charge excitations. On the other hand, the approximation fails, even qualitatively, for quantities for which backscattering is important, i.e., those quantities which are crucial for an accurate description of transport. In particular, the Drude weight in the presence of a single impurity is discussed.