Transient-estimate Monte Carlo in the two-dimensional electron gas.

Energies of the ground state and low-lying excited states of the two-dimensional electron gas have been calculated by a transient-estimate Monte Carlo method. This is an exact fermion quantum Monte Carlo method that systematically improves upon the results of a variational energy without imposing nodal constraints. We focus upon the density rs51, where our previous variational Monte Carlo calculation found qualitative differences in the effective mass from other theoretical approaches. Starting from a wave function with backflow and two-body correlations, the best trial function in our previous variational study, we find a ground-state energy only very slightly lower than the previously reported backflow fixed-node energy, reinforcing the conclusion that backflow wave functions are quite accurate. The effective mass derived from excitation energies does not differ significantly from the variational Monte Carlo results, giving a value of m*/m50.9360.01, so we conclude that the effective mass is indeed less than bare electron mass for a range of densities around rs51.