A quantum Monte Carlo study of the two-dimensional electron gas

Quantum Monte Carlo has recently made great progress as a computational tool for quantum many-body systems. We have extended previous Monte Carlo methods to study both ground state and excited states of the two-dimensional electron gas. For ground state properties we have used variational and fixed-node diffusion Monte Carlo methods, the latter of which is a nearly exact method for a system of many fermions. With introduction of backflow and three-body correlations, we find significant improvements in both variational and fixed-node energies over the Slater-Jastrow results which consider only two-body correlations. It is found that the backflow effect is dominant over the three-body effect at high density ($r\sb{s} \sim 1)$ while they are of equal importance at the lowest density considered $(r\sb{s} \sim 20)$. The effects are comparable to those in bulk $\sp3$He. The numerical results are used to provide an analytic expression for the correlation energy of the two-dimensional electron gas as a function of the density. For particle-hole excitations of the system, variational Monte Carlo is employed. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi liquid parameters and related physical quantities such as the effective mass and Lande g factor of the two-dimensional electron gas, which are compared with previous analytic calculations. Finally, the validity of our fixed-node calculations for the ground state and variational ones for the excitations is tested by transient-estimate calculations, which allow for relaxation of the fixed-node conditions.U of I OnlyETDs are only available to UIUC Users without author permissio