Exact ground state properties of the one-dimensional Coulomb gas

TL;DR

This paper presents an exact analysis of the ground state properties of a one-dimensional Coulomb gas using Bose-Fermi mapping and diffusion Monte Carlo, revealing different excitation modes and density profiles.

Contribution

It introduces an exact method to compute ground state properties of 1D Coulomb gases, overcoming the Fermi sign problem and comparing density profiles with local density approximation.

Findings

Exact ground state energy computed for homogeneous and trapped systems.

Identification of plasmon excitations in the low-density limit.

Density profile transition from semicircular to inverted parabola with increasing charge.

Abstract

The ground state properties of a single-component one-dimensional Coulomb gas are investigated. We use Bose-Fermi mapping for the ground state wave function which permits to solve the Fermi sign problem in the following respects (i) the nodal surface is known, permitting exact calculations (ii) evaluation of determinants is avoided, reducing the numerical complexity to that of a bosonic system, thus allowing simulation of a large number of fermions. Due to the mapping the energy and local properties in one-dimensional Coulomb systems are exactly the same for Bose-Einstein and Fermi-Dirac statistics. The exact ground state energy has been calculated in homogeneous and trapped geometries by using the diffusion Monte Carlo method. We show that in the low-density Wigner crystal limit an elementary low-lying excitation is a plasmon, which is to be contrasted with the large-density ideal Fermi gas/Tonks-Girardeau limit, where low lying excitations are phonons. Exact density profiles are confronted to the ones calculated within the local density approximation which predicts a change from a semicircular to inverted parabolic shape of the density profile as the value of the charge is increased.