Consistency of potential energy in the dynamical vertex approximation

TL;DR

This paper introduces a method to resolve ambiguities in potential energy calculations within the ladder dynamical vertex approximation by incorporating an effective mass renormalization, improving agreement with other methods and restoring energy hierarchies.

Contribution

It proposes a novel approach using charge and spin susceptibility renormalization to achieve consistent potential energy calculations in ladder DΓA.

Findings

More accurate transition temperature predictions aligning with other methods.

Lower potential energy values compared to DMFT and non-self-consistent ladder DΓA.

Restoration of kinetic energy hierarchy in weak coupling regime.

Abstract

In the last decades, dynamical mean-field theory (DMFT) and its diagrammatic extensions have been successfully applied to describe local and nonlocal correlation effects in correlated electron systems. Unfortunately, except for the exact solution, it is impossible to fulfill both the Pauli principle and conservation laws at the same time. Consequently, fundamental observables such as the kinetic and potential energies are ambiguously defined. In this work, we propose an approach to overcome the ambiguity in the calculation of the potential energy within the ladder dynamical vertex approximation (D$\Gamma$A) by introducing an effective mass renormalization parameter in both the charge and the spin susceptibility of the system. We then apply our method to the half-filled single-band Hubbard model on a three-dimensional bipartite cubic lattice. We find that: (i) at weak-to-intermediate coupling, a reasonable modification of the transition temperature $\TN$ to the antiferromagnetically ordered state with respect to previous ladder D$\Gamma$A calculations without charge renormalization. This is in good agreement with dual fermion and Monte Carlo results; (ii) the renormalization of charge fluctuations in our new approach leads to a unique value for the potential energy which is substantially lower than corresponding ones from DMFT and non-self-consistent ladder D$\Gamma$A; and (iii) the hierarchy of the kinetic energies between the DMFT and the ladder D$\Gamma$A in the weak coupling regime is restored by the consideration of charge renormalization.