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In the last decades, dynamical mean-field theory (DMFT) and its diagrammaticextensions have been successfully applied to describe local and nonlocalcorrelation effects in correlated electron systems. Unfortunately, except forthe exact solution, it is impossible to fulfill both the Pauli principle andconservation laws at the same time. Consequently, fundamental observables suchas the kinetic and potential energies are ambiguously defined. In this work, wepropose an approach to overcome the ambiguity in the calculation of thepotential energy within the ladder dynamical vertex approximation (D$\Gamma$A)by introducing an effective mass renormalization parameter in both the chargeand the spin susceptibility of the system. We then apply our method to thehalf-filled single-band Hubbard model on a three-dimensional bipartite cubiclattice. We find that: (i) at weak-to-intermediate coupling, a reasonablemodification of the transition temperature $\TN$ to the antiferromagneticallyordered state with respect to previous ladder D$\Gamma$A calculations withoutcharge renormalization. This is in good agreement with dual fermion and MonteCarlo results; (ii) the renormalization of charge fluctuations in our newapproach leads to a unique value for the potential energy which issubstantially lower than corresponding ones from DMFT and non-self-consistentladder D$\Gamma$A; and (iii) the hierarchy of the kinetic energies between theDMFT and the ladder D$\Gamma$A in the weak coupling regime is restored by theconsideration of charge renormalization.

Consistency of potential energy in the dynamical vertex approximation