  We report the quantum phase diagram of a one-dimensional Coulomb wire
obtained using the path integral Monte Carlo (PIMC) method. The exact knowledge
of the nodal points of this system permits us to find the energy in an exact
way, solving the sign problem which spoils fermionic calculations in higher
dimensions. The results obtained allow for the determination of the stability
domain, in terms of density and temperature, of the one-dimensional Wigner
crystal. At low temperatures, the quantum wire reaches the quantum-degenerate
regime, which is also described by the diffusion Monte Carlo method. Increasing
the temperature the system transforms to a classical Boltzmann gas which we
simulate using classical Monte Carlo. At large enough density, we identify a
one-dimensional ideal Fermi gas which remains quantum up to higher temperatures
than in two- and three-dimensional electron gases. The obtained phase diagram
as well as the energetic and structural properties of this system are relevant
to experiments with electrons in quantum wires and to Coulomb ions in
one-dimensional confinement.
