arXiv subjects
Publications and source records attributed to F. Delyon.
We present a simple approach to the fixed phase method in Quantum Monte Carlo. This applies to electrons in molecules and electron gas and is straightforwardly extended to the Schrödinger equation with magnetic field.
Studying the jellium model in the Hartree-Fock approximation, Overhauser has shown that spin density waves (SDW) can lower the energy of the Fermi gas, but it is still unknown if these SDW are actually relevant for the phase diagram. In this paper, we give a more complete description of SDW states. We show that a modification of the Overhauser ansatz explains the behavior of the jellium at high density compatible with previous Hartree-Fock simulations.
In a previous letter, L. Baguet et al., (Phys. Rev. Lett. {\bf 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 strongly supporting 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, rs> 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 consider the three-dimensional electron gas confined by a strictly two-dimensional homogeneous positive charge density at $z=0$. Within the Hartree-Fock approximation, we study the mode structure in the confined direction in the metallic regime. We find, that for $r_s<1.3$ ($r_s<2.5$) the unpolarized (polarized) electron gas starts to populate also the first excited state in the $z$-direction.
We determine the ground state of the two-dimensional, fully polarized electron gas within the Hartree-Fock approximation without imposing any particular symmetries on the solutions. At low electronic densities, the Wigner crystal solution is stable, but for higher densities ($r_s$ less than $\sim 3$) we obtain a ground state of different symmetry: the charge density forms a triangular lattice with about 11% more sites than electrons. We argue that this conducting state with broken translational symmetry remains the ground state of the high density region in the thermodynamic limit giving rise to a metal to insulator transition.
We consider the ground state of the homogeneous electron gas and we prove that a Hartree-Fock solution, motivated by previous simulations, has lower energy than the Fermi gas in the large density limit. This solution is a metallic phase : the density modulation corresponds to a partially occupied crystal (the number of sites is larger than the number of electrons).