Ground state properties of the one dimensional Coulomb gas

TL;DR

This paper investigates the ground state properties of a quasi-one-dimensional electron gas with Coulomb interactions, using advanced Monte Carlo methods to accurately compute correlation energies and compare with Luttinger liquid predictions.

Contribution

The study provides a new parametrization of the correlation energy for quasi-one-dimensional systems and demonstrates the effectiveness of lattice regularized diffusion Monte Carlo in low-density regimes.

Findings

Accurate correlation energy parametrization for various widths

Qualitative agreement with Luttinger liquid model

Effective local density energy functional for quasi-1D systems

Abstract

We study the ground state properties of a quasi one dimensional electron gas, interacting via an effective potential with a harmonic transversal confinement and long range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows to sample the exact ground state of the system, even in the low density regime when the exchange between electrons is extremely small. For different values of the width parameter b (0.1 a*_0 <= b <= 4 a*_0), we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi one dimensional systems. Moreover we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long range interactions.