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

TL;DR

This paper presents an ab initio method to accurately study Wigner localization of two electrons in low-density regimes in two and three dimensions, using exact diagonalization and innovative boundary conditions.

Contribution

The authors develop a new computational approach combining Clifford boundary conditions and Gaussian orbitals to precisely capture Wigner localization phenomena.

Findings

Successful observation of Wigner localization at very low densities

Validation of the method against a semi-classical model

Efficient calculation leveraging translational symmetry

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.