Lower Bound on the Hartree-Fock Energy of the Electron Gas

Abstract

The Hartree-Fock ground state of the Homogeneous Electron Gas is never translation invariant, even at high densities. As proved by Overhauser, the (paramagnetic) free Fermi Gas is always unstable under the formation of spin or charge density waves. We give here the first explicit bound on the energy gain due to the breaking of translational symmetry. Our bound is exponentially small at high density, which justifies posteriori the use of the non-interacting Fermi Gas as a reference state in the large-density expansion of the correlation energy of the Homogeneous Electron Gas. We are also able to discuss the positive temperature phase diagram and prove that the Overhauser instability only occurs at temperatures which are exponentially small at high density. Our work sheds a new light on the Hartree-Fock phase diagram of the Homogeneous Electron Gas.

arXiv commentExtended version. Includes a new estimate on the critical temperature

References in corpus (23)

• Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas
• The Uniform Electron Gas at Warm Dense Matter Conditions
• {\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit
• Ab initio thermodynamic results for the degenerate electron gas at finite temperature
• Spin Polarization of the Low Density 3D Electron Gas
• Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals
• Momentum Distribution and Renormalization Factor in Sodium and the Electron Gas
• Fermionic path integral Monte Carlo results for the uniform electron gas at finite temperature
• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics
• The BCS functional of superconductivity and its mathematical properties
• The Hartree-Fock ground state of the three-dimensional electron gas
• The Hartree-Fock phase diagram of the two-dimensional electron gas
• A Nonlinear Model for Relativistic Electrons at Positive Temperature
• Hartree-Fock Ground State Phase Diagram of Jellium
• Metal-insulator transition in the two-dimensional fully polarized homogeneous electron gas from Hartree-Fock solutions
• Metal-insulator transition in the Hartree-Fock phase diagram of the fully polarized homogeneous electron gas in two dimensions
• Energy Cost to Make a Hole in the Fermi Sea
• Properties of Hartree-Fock solutions of the three-dimensional electron gas
• The BCS gap equation for spin-polarized fermions
• Upper bounds of spin-density wave energies in the homogeneous electron gas
• General pairing mechanisms in the BCS-theory of superconductivity

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• The Gell-Mann$-$Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime
• Seven Useful Questions in Density Functional Theory
• On the Effective Quasi-Bosonic Hamiltonian of the Electron Gas: Collective Excitations and Plasmon Modes
• Weak coupling limit for Schrödinger-type operators with degenerate kinetic energy for a large class of potentials
• Bosonic Collective Excitations in Fermi Gases
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• Localization and IDS Regularity in the Disordered Hubbard Model within Hartree-Fock Theory
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• Homogeneous Electron Liquid in Arbitrary Dimensions: Exchange and Correlation Using the Singwi-Tosi-Land-Sjölander Approach
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