Spectral moments in the homogeneous electron gas

Abstract

We present calculations of the lowest three moments of the spectral function of the one-particle Green's function of the unpolarized three-dimensional homogeneous electron gas, which are related to the exact ground-state properties via commutation relations. The moments are, in turn, related to the coefficients in the expansion of the self-energy in inverse powers of the frequency. The zeroth-order term in this expansion can be written in terms of the momentum distribution function, while the first-order term consists of a local term which can be written in terms of the pair correlation function or static structure factor, and a nonlocal term. We use data from diffusion quantum Monte Carlo calculations to evaluate the zeroth-order term and the local part of the first-order term. We have also examined local-field approximations to the self-energy, finding that they do not affect the zeroth-order term in the high-energy expansion, but they substantially alter the first-order term. The nonlocal part of the second-order term has been evaluated using a wave function consisting of a single determinant of plane waves. Our results provide additional benchmarks for self-energy theories of the homogeneous electron gas.