The ground state properties of a single-component one-dimensional Coulomb gasare investigated. We use Bose-Fermi mapping for the ground state wave functionwhich permits to solve the Fermi sign problem in the following respects (i) thenodal surface is known, permitting exact calculations (ii) evaluation ofdeterminants is avoided, reducing the numerical complexity to that of a bosonicsystem, thus allowing simulation of a large number of fermions. Due to themapping the energy and local properties in one-dimensional Coulomb systems areexactly the same for Bose-Einstein and Fermi-Dirac statistics. The exact groundstate energy has been calculated in homogeneous and trapped geometries by usingthe diffusion Monte Carlo method. We show that in the low-density Wignercrystal limit an elementary low-lying excitation is a plasmon, which is to becontrasted with the large-density ideal Fermi gas/Tonks-Girardeau limit, wherelow lying excitations are phonons. Exact density profiles are confronted to theones calculated within the local density approximation which predicts a changefrom a semicircular to inverted parabolic shape of the density profile as thevalue of the charge is increased.
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