A strongly correlated electron state at one-dimensional quantum points

The method of exact diagnoalization is applied to find the distribution of electrons over single-particle states at a 1D quantum point and the Fourier spectrum of the electron density. It is shown that the distribution function contains an unexpected signularity at the Fermi level. It is found that (i) the singularity results from the Wigner electron ordering and (ii) the Wigner ordering involves suppression of spatial Fourier harmonics of the electron density observed when the interaction potential grows over the entire range of wave vectors except for the double Fermi wave vector. It is demonstrated that the distribution function calculated within the Luttinger model also has a singularity at the Fermi level and this singularity is of an irregular shape.