Vieira and co-workers 158 have investigated the charge density and magnetization density profiles of one-dimensional metals using two complementary many-body methods: numerically exact (Lanczos) diagonalization and the Bethe-Ansatz local-density approximation, both with and without a simple self-interaction correction. They found that, depending on the magnetization of the system, local approximations could reproduce different Fourier components of the exact Friedel oscillations. We should stress that the oscillatory pattern obtained by Vieira et al. (see Fig. ) shows a very similar character to the atom-wise charge alternating oscillation for polyenes (Fig. ). We believe this stems from the similarity between the electron systems.