Wigner localization in two and three dimensions: an \emph{ab initio} approach

Abstract

In this work we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on Clifford periodic boundary conditions with a renormalized distance in the Coulomb potential. To accurately represent the electronic wave function we use a regular distribution in space of gaussian-type orbitals and we take advantage of the translational symmetry of the system to efficiently calculate the electronic wave function. We are thus able to accurately describe the wave function up to very low density. We validate our approach by comparing our results to a semi-classical model that becomes exact in the low-density limit. With our approach we are able to observe the Wigner localization without ambiguity.

References in corpus (5)

• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• Strong correlation in Kohn-Sham density functional theory
• Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals
• Ground state of two electrons on a sphere
• Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes