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

TL;DR

This study uses variational Monte Carlo methods to analyze charge and spin correlations in a one-dimensional continuum electron gas with long-range interactions, revealing good agreement with theoretical models despite sampling challenges.

Contribution

It introduces an effective approach to overcome sampling issues in 1D electron gas simulations and validates results against Luttinger liquid predictions.

Findings

Good agreement with Luttinger model predictions

Effective handling of non-ergodic sampling issues

Detailed analysis of structure factors in 1D electron systems

Abstract

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.