First-Principles Calculations of Quasiparticle Excitations of Open-Shell Condensed Matter Systems

We develop a Green’s function approach to quasiparticle excitations of open-shell systems within the $GW$ approximation. It is shown that accurate calculations of the characteristic multiplet structure require a precise knowledge of the self-energy and, in particular, its poles. We achieve this by constructing the self-energy from appropriately chosen mean-field theories on a fine frequency grid. We apply our method to a two-site Hubbard model, several molecules, and the negatively charged nitrogen-vacancy defect in diamond and obtain good agreement with experiment and other high-level theories.

Figure 1

Self-energy ${\Sigma }_{jj}(\omega )$ and spectral function $A_{jj}(\omega )$ for (a) the removal of a down-spin electron from the $j=4b_2$ orbital in ${\mathrm{NO}}_2$ and (b) the removal of an up-spin electron from the $j=4b_2$ orbital. A Lorentzian broadening of 20 meV is used for each curve.

Figure 2

Self-energy ${\Sigma }_{jj}(\omega )$ and spectral function $A_{jj}(\omega )$ for the removal of an up-spin electron from the $j=\nu$ defect orbital of an ${\mathrm{NV}}^{-1}$ center in diamond. A Lorentzian broadening of 5 meV is used for each curve.