Phase diagram of a quantum Coulomb wire

TL;DR

This paper maps the quantum phase diagram of a one-dimensional Coulomb wire using Monte Carlo methods, revealing the stability of the Wigner crystal and quantum-degenerate regimes at various densities and temperatures.

Contribution

It provides the first exact phase diagram of a 1D Coulomb wire by solving the sign problem through known nodal points, combining quantum and classical Monte Carlo techniques.

Findings

Identification of the stability domain of the 1D Wigner crystal.

Determination of the quantum-degenerate regime at low temperatures.

Discovery of a 1D ideal Fermi gas at high densities.

Abstract

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.