GW-RPA studies of interacting electron gas models

In this work, we study the ground states and single-particle excitation spectra of both two dimensional (2D) and three dimensional (3D) electron-gas models with quadratic band dispersions using many-body perturbation methods. We start with unrestricted Hartree-Fock calculations that may lead to either Wigner crystal or Fermi liquid state at low carrier densities, and we further calculate the GW quasi-particle energies based on the two different types of ground states. The correlation energy is treated with random phase approximation (RPA) based on the GW quasi-particle energies. We apply such Hartree-Fock+GW+RPA method to study the Wigner crystal transitions in both 2D and 3D interacting electron-gas models, and demonstrate that the critical Wigner-Seitz radii can be more accurately determined compared to the bare Hartree-Fock methods.