Effects of Confinement Potential and Screening on a Quasi One Dimensional Electron Gas

We study a quasi one dimensional system of electrons for different densities and strengths of the transverse confining potential. By means of exact quantum Monte Carlo techniques, we analyze the behavior of electrons interacting via an unscreened potential with a long range $1/r$ tail. We also study the effect of screening due to a metallic gate, which allows a more direct comparison with experiments. \vskip 0.1cm While the high density regime is well described by the RPA, we find that the charge compressibility $\chi_c$ is reduced due to electronic correlation as the density decreases. In the absence of screening, this corresponds to the onset of a quasi Wigner crystal, as shown by the finite size scaling of the static structure factor at 4k$_f$. As the density decreases further, the electrons behave as spinless fermions which is evidenced by the energetics and exponentially small spin velocities. The spinless fermion features persist also in the strongly screened system, and the RPA to Wigner crystal crossover is shifted to higher densities for a thinner wire.