A Finite Element Configuration Interaction Method for Wigner Localization

TL;DR

This paper introduces a finite element configuration interaction method to accurately simulate Wigner localization in low-density electron systems, capturing strong correlations and electron localization phenomena.

Contribution

It presents a novel numerical algorithm combining finite element discretization, a strongly correlated initial state, and a selected CI approach for studying Wigner molecules.

Findings

Efficient simulation of Wigner localization in quantum wires and dots.

Accurate capture of electron localization and correlation effects.

Demonstrated effectiveness of the method through numerical experiments.

Abstract

The Wigner localization is an electron phase at low densities when the electrons are sharply localized around equilibrium positions. The simulation of the Wigner localization phenomenon requires careful treatment of the many-body correlations, as the electron-electron interaction dominates the system. This work proposes a numerical algorithm to study the electron ground states of the Wigner molecules. The main features of our algorithm are three-fold: (i) a finite element discretization of the one-body space such that the sharp localization can be captured; (ii) a good initial state obtained by exploiting the strongly correlated limit; and (iii) a selected configuration interaction method by choosing the Slater determinants from (stochastic) gradients. Numerical experiments for some typical one-dimensional quantum wires and two-dimensional circular quantum dots are provided to show the efficiency of our algorithm.