A Finite Element Configuration Interaction Method for Wigner Localization

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.