Study of two-dimensional electron systems in the renormalized-ring-diagram approximation

With a super-high-efficient numerical algorithm, we are able to self-consistently calculate the Green's function in the renormalized-ring-diagram approximation for a two-dimensional electron system with long-range Coulomb interactions. The obtained ground-state energy is found to be in excellent agreement with that of the Monte Carlo simulation. The numerical results of the self-energy, the effective mass, the distribution function, and the renormalization factor of the Green's function for the coupling constants in the range $0 \le r_s \le 30$ are also presented.