Charge and spin correlations of a one dimensional electron gas on the continuum

We present a variational Monte Carlo study of a model one dimensional electron gas on the continuum, with long-range interaction (1/r decay). At low density the reduced dimensionality brings about pseudonodes of the many-body wavefunction, yielding non-ergodic behavior of naive Monte Carlo sampling, which affects the evaluation of pair correlations and the related structure factors. The problem is however easily solved and we are able to carefully analyze the structure factors obtained from an optimal trial function, finding good agreement with the exact predictions for a Luttinger-like hamiltonian with an interaction similar to the one used in the present study.