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 r(s)=1, 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*/m=0.93+/-0.01, so we conclude that the effective mass is indeed less than bare electron mass for a range of densities around r(s)=1.