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Energy functionals of the Green's function can simultaneously providespectral and thermodynamic properties of interacting electrons' systems. Thoughpowerful in principle, these formulations need to deal with dynamical(frequency-dependent) quantities, increasing the algorithmic and numericalcomplexity and limiting applications. We first show that, when representing allfrequency-dependent propagators as sums over poles, the typical operations ofdynamical formulations become closed (i.e., all quantities are expressed assums over poles) and analytical. Importantly, we map the Dyson equation into anonlinear eigenvalue problem that can be solved exactly; this is achieved byintroducing a fictitious non-interacting system with additional degrees offreedom which shares, upon projection, the same Green's function of the realsystem. Last, we introduce an approximation to the exchange-correlation part ofthe Klein functional adopting a localized $GW$ approach; this is ageneralization of the static Hubbard extension of density-functional theorywith a dynamical screened potential $U(\omega)$. We showcase the algorithmicefficiency of the methods, and the physical accuracy of the functional, bycomputing the spectral, thermodynamic, and vibrational properties of SrVO$_3$,finding results in close agreement with experiments and state-of-the-artmethods, at highly reduced computational costs and with a transparent physicalinterpretation.

Energies and spectra of solids from the algorithmic inversion of dynamical Hubbard functionals