Spectral functions of the uniform electron gas via coupled-cluster theory and comparison to the $GW$ and related approximations

We use 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.

Figure 1

Spectral functions for the UEG with $r_{\mathrm{s}}=4.0$ using a supercell containing 14 electrons in 19 spatial orbitals. (a) For the $\mathit{k}=(0,0,0)$ state, the spectral function exhibits a prominent satellite peak; the $\mathrm{HF}+GW$ result has been scaled down by a factor of 1.5. (b) For the highest occupied state at $\mathit{k}=(2\pi /L,0,0)$, the spectral function exhibits a strong quasiparticle peak with a very weak satellite structure; the satellite region between $-18$ and $-7$ eV has been magnified by a factor of 30. A linewidth broadening of $\eta =0.2$ eV is used in all calculations.

Figure 2

(a) Spectral function of the $\mathit{k}=(0,0,0)$ state of the UEG with $r_{\mathrm{s}}=4.0$ and 114 electrons in 485 orbitals. The HF+$GW$ result is scaled down by a factor of 1.5 and a linewidth broadening of $\eta =0.8$ eV is used in all calculations. (b) Comparison of the spectral functions of the $\mathit{k}=(0,0,0)$ state in the thermodynamic limit (solid curves) and the 114 electron system (dashed curves) from LDA+$GW$ (blue curves) and LDA+$GW$+C (green curves). (c) Complete basis set limit quasiparticle energies as a function of wave vector for the 114 electron system (symbols) and quadratic fits (dashed curves).