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arXiv:1404.7652 · Physical Review B

Properties of Hartree-Fock solutions of the three-dimensional electron gas

Lucas Baguet, Fran�ois Delyon, B. Bernu, Markus Holzmann

Published Oct 23, 2014• 14 citations
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Abstract

In a previous paper, Baguet et al. [Phys. Rev. Lett. 111, 166402 (2013)], we presented the ground-state phase diagram of the homogeneous electron gas in three dimensions within the Hartree-Fock approximation yielding incommensurate crystal states at high density. Here, we analyze the properties of these solutions. In particular, at high density we find universal behavior of the incommensurate crystal, which strongly supports the existence of a spin-density-wave ground state.

DOI
10.1103/physrevb.90.165131

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In a previous paper, Baguet et al. [Phys. Rev. Lett. 111, 166402 (2013)], we presented the ground-state phase diagram of the homogeneous electron gas in three dimensions within the Hartree-Fock approximation yielding incommensurate crystal states at high density. Here, we analyze the properties of these solutions. In particular, at high density we find universal behavior of the incommensurate crystal, which strongly supports the existence of a spin-density-wave ground state.
We calculate the ground-state phase diagram of the homogeneous electron gas in two dimensions within the Hartree-Fock approximation. At high density, we find stable solutions, where the electronic charge and spin density form an incommensurate crystal having more crystal sites than electrons, whereas the commensurate Wigner crystal is favored at lower densities, ${r}_{s}\ensuremath{\gtrsim}1.22$. Our explicit calculations demonstrate that the homogeneous Fermi-liquid state, though being an exact stationary solution of the Hartree-Fock equations, is never the Hartree-Fock ground state of the electron gas.
We calculate the ground state phase diagram of the homogeneous electron gas in three dimensions within the Hartree-Fock approximation and show that broken symmetry states are energetically favored at any density against the homogeneous Fermi gas state with isotropic Fermi surface. At high density, we find metallic spin-unpolarized solutions where electronic charge and spin density form an incommensurate crystal having more crystal sites than electrons. For r(s)→0, our solutions approach pure spin-density waves, whereas the commensurate Wigner crystal is favored at lower densities, r(s)≳3.4. Decreasing the density, the system undergoes several structural phase transitions with different lattice symmetries. The polarization transition occurs around r(s)≈8.5.
In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is unstable to a spin-density wave state. Determining the true HF ground state has remained a challenge. Using numerical calculations for finite systems and analytic techniques, we study the unrestricted HF ground state of the three-dimensional electron gas. At high density, we find broken spin symmetry states with a nearly constant charge density. Unlike previously discussed spin wave states, the observed wave vector of the spin-density wave is smaller than 2k(F). The broken-symmetry state originates from pairing instabilities at the Fermi surface, a model for which is proposed.
In this paper, we review the possibility of periodic ground states of the two‐ and three‐dimensional electron gas at high and intermediate densities. At the Hartree–Fock level, we obtain explicit solutions at all densities having lower energies than the homogeneous Fermi gas. In the high‐density region, the electrons only partially fill up the band approaching spin density waves as predicted by Overhauser. Preliminary variational Monte Carlo calculations on the polarized two‐dimensional electron gas confirm the existence of these new types of ground states.
Ground-state properties of the two-dimensional Hubbard model with point-defect disorder are investigated numerically in the Hartree-Fock approximation. The phase diagram in the p(point defect concentration)--\ensuremath{\delta}(deviation from half filling) plane exhibits antiferromagnetic, spin-density-wave, paramagnetic, and spin-glass-like phases. The disorder stabilizes the antiferromagnetic phase relative to the spin-density-wave phase. The presence of U strongly enhances the localization in the antiferromagnetic phase. The spin-density-wave and spin-glass-like phases are weakly localized.