  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.
