Correlations in a two-dimensional quantum electron gas with ln(r) interactions

Abstract

The authors have examined some aspects of the ground state of a quantum two-dimensional electron gas interacting with ln(r) potential. It is shown that the divergence appearing in the Hartree-Fock contribution to the ground-state energy exactly cancels the divergence in the electrostatic contribution. The next leading contribution to the ground-state energy is explicitly calculated and is also found to be finite. Further, the exact asymptotic expression for the structure factor at large wavevectors is obtained using the exact asymptotic solution of the two-electron Schrodinger equation for small separation r.