Method of effective-potential expansion for the many-body problem: Two-dimensional electron gas in two-body approximation

Following previous work in which a variational method for the many-body problem was proposed wherein an effective potential $\tilde{V}$ was introduced as a variational parameter to construct a trial wave function, we apply the method to the two-dimensional electron gas. In the method, every physical quantity is expanded in powers of $\tilde{V}$ instead of the bare potential as in the usual perturbation-theoretic approach. Because of this choice of expansion parameter, the expansion series converges rapidly even in the strong-coupling region. The result for the correlation energy in the two-dimensional electron gas agrees very well with that given by the variational Monte Carlo method even in the lowest-order calculation (i.e., to second order in $\tilde{V}$). The difference is within several percent for $1<\mathrm{}{r}_s<100\mathrm{}$.