Variational Diagrammatic Monte-Carlo Built on Dynamical Mean-Field Theory Starting Point

We develop a variational perturbation expansion around dynamical mean-field theory (DMFT) propagators, which systematically adds nonlocal correlations to the local correlations treated by DMFT. By introducing long-range magnetic order, our approach is applied to investigate both paramagnetic and antiferromagnetic states in the three-dimensional cubic Hubbard model at half-filling, calculating the Néel temperature, magnetization, energy, and specific heat. With a few orders of perturbation, we successfully predict the Néel temperature across the Slater to Mott-Heisenberg regimes for all correlation strengths. Our results confirm small corrections to DMFT solutions in the weak interaction regime in 3D, while bringing significant corrections to magnetic, thermodynamic, and spectral properties in the intermediate correlation regime.