Ground state of the fermion one-component plasma: A Monte Carlo study in two and three dimensions

TLDR

We used fermion Monte Carlo variational calculations to compute the equation of state of the uniform electron one‑component plasma in two and three dimensions, examining Wigner crystal, unpolarized fluid, and polarized fluid phases. The Monte Carlo results yield highly accurate ground‑state excess energies that agree with previous studies, showing that the Wigner crystal has the lowest energy for rs > 67 (3D) and rs > 33 (2D), the polarized fluid is stable for 26 < rs < 67 (3D) and 13 < rs < 33 (2D), while the unpolarized fluid dominates at higher densities, and a parameter‑free RPA pseudopotential reproduces these energies, supporting the conjecture that the electron gas ground state is spin‑polarized at intermediate densities.

Abstract

We have performed fermion Monte Carlo variational calculations to determine the equation of state of the uniform electron one-component plasma in two and three dimensions. The ground-state excess energies calculated by the Monte Carlo method are very precise and in agreement with those of other calculations in the metallic density range and in the very-low-density Wigner crystals. Three phases have been investigated: the Wigner crystal, the normal or unpolarized fluid, and the polarized fluid. The Wigner crystal has the lowest energy for ${r}_{s}>67$ in three dimensions and ${r}_{s}>33$ in two dimensions. The totally polarized quantum fluid is stable for $26<{r}_{s}<67$ in three dimensions and for $13<{r}_{s}<33$ in two dimensions, and the normal or unpolarized fluid is stable at higher densities ${r}_{s}<26$ in three dimensions and ${r}_{s}<13$ in two dimensions. A pseudopotential with no adjustable parameters, derived from the random-phase approximation, is found to give excellent energies. The present results lend support to earlier conjectures that the ground state of the electron gas will be spin polarized at intermediate densities.