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

TL;DR

This paper introduces a highly efficient numerical method to self-consistently compute properties of two-dimensional electron systems with Coulomb interactions, achieving results that align well with Monte Carlo simulations.

Contribution

It presents a novel, efficient numerical algorithm for the renormalized-ring-diagram approximation, enabling detailed analysis of 2D electron systems with improved accuracy.

Findings

Ground-state energy matches Monte Carlo results

Calculated effective mass and renormalization factors across coupling range

Provided detailed Green's function properties for various interaction strengths

Abstract

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.