Spectral Functions of the Uniform Electron Gas via Coupled-Cluster Theory and Comparison to the $GW$ and Related Approximations

We use, for the first time, ab initio coupled-cluster theory to compute the spectral function of the uniform electron gas at a Wigner-Seitz radius of $r_{\mathrm{s}}=4$. The coupled-cluster approximations we employ go significantly beyond the diagrammatic content of state-of-the-art $GW$ theory. We compare our calculations extensively to $GW$ and $GW$-plus-cumulant theory, illustrating the strengths and weaknesses of these methods in capturing the quasiparticle and satellite features of the electron gas. Our accurate calculations further allow us to address the long-standing debate over the occupied bandwidth of metallic sodium. Our findings indicate that the future application of coupled-cluster theory to condensed phase material spectra is highly promising.